Force
NCERT - Laws of Motion
NCERT - Laws of Motion - Exemplar Problem
1
A book is at rest in space, and there are no planets or stars nearby. What are the forces acting on the book?
Practice
A
No force acts on the book.
B
Only gravitational force acts on the book.
C
Only frictional force acts on the book.
D
Both gravitational force and frictional force act on the book.
ā Show Answer
ā Correct Answer:
A
(No force acts on the book.)
š” Explanation
Given:
The book is at rest in space.
There are no planets or stars nearby.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest or continues in uniform motion unless an unbalanced external force acts on it.
Since there are no planets or stars nearby, no significant gravitational force acts on the book.
There is also no surface in space, so no frictional force acts on the book.
Therefore, no external force is considered to act on the book.
Conclusion:
No force acts on the book.
The book is at rest in space.
There are no planets or stars nearby.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest or continues in uniform motion unless an unbalanced external force acts on it.
Since there are no planets or stars nearby, no significant gravitational force acts on the book.
There is also no surface in space, so no frictional force acts on the book.
Therefore, no external force is considered to act on the book.
Conclusion:
No force acts on the book.
2
A book is moving with constant velocity in space, and there are no planets or stars nearby. What will happen to the book if no external force acts on it?
Practice
A
The book will continue moving with constant velocity in a straight line.
B
The book will gradually slow down and stop.
C
The book will suddenly change its direction.
D
The book will start accelerating.
ā Show Answer
ā Correct Answer:
A
(The book will continue moving with constant velocity in a straight line.)
š” Explanation
Given:
The book is moving with constant velocity.
There are no planets or stars nearby.
No external force acts on the book.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object in motion continues to move with constant velocity in a straight line unless an unbalanced external force acts on it.
Since no external force acts on the book, there is nothing to change its speed or direction.
Therefore:
The book will continue moving with constant velocity in a straight line.
The book is moving with constant velocity.
There are no planets or stars nearby.
No external force acts on the book.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object in motion continues to move with constant velocity in a straight line unless an unbalanced external force acts on it.
Since no external force acts on the book, there is nothing to change its speed or direction.
Therefore:
The book will continue moving with constant velocity in a straight line.
3
A book is at rest on the surface of the Earth. What are the forces acting on the book?
Practice
A
Only gravitational force acts on the book.
B
Only normal force acts on the book.
C
Gravitational force acts downward and normal force from the surface acts upward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
C
(Gravitational force acts downward and normal force from the surface acts upward.)
š” Explanation
Given:
The book is at rest on the surface of the Earth.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The table or ground exerts an equal and opposite normal force upward on the book.
These two forces balance each other, so the net force on the book is zero.
Therefore:
Gravitational force acts downward and normal force from the surface acts upward.
The book is at rest on the surface of the Earth.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The table or ground exerts an equal and opposite normal force upward on the book.
These two forces balance each other, so the net force on the book is zero.
Therefore:
Gravitational force acts downward and normal force from the surface acts upward.
4
A book is moving with uniform velocity on the surface of the Earth. What are the forces acting on the book if friction is neglected?
Practice
A
Only gravitational force acts on the book.
B
Only normal force acts on the book.
C
Gravitational force acts downward and normal force acts upward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
C
(Gravitational force acts downward and normal force acts upward.)
š” Explanation
Given:
The book is moving with uniform velocity on the surface of the Earth.
Friction is neglected.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object continues to move with constant velocity when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The surface exerts an equal and opposite normal force upward on the book.
Since these forces balance each other, the net force is zero and the book continues moving with uniform velocity.
Therefore:
Gravitational force acts downward and normal force acts upward.
The book is moving with uniform velocity on the surface of the Earth.
Friction is neglected.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object continues to move with constant velocity when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The surface exerts an equal and opposite normal force upward on the book.
Since these forces balance each other, the net force is zero and the book continues moving with uniform velocity.
Therefore:
Gravitational force acts downward and normal force acts upward.
5
A book is kept inside a lift, and the lift is at rest on the 5th floor. What are the forces acting on the book?
Practice
A
Only gravitational force acts on the book.
B
Only normal force acts on the book.
C
Gravitational force acts downward and normal force from the lift floor acts upward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
C
(Gravitational force acts downward and normal force from the lift floor acts upward.)
š” Explanation
Given:
The book is inside a lift.
The lift is at rest on the 5th floor.
The book is also at rest relative to the lift.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The floor of the lift exerts an equal and opposite normal force upward on the book.
Since the lift is at rest, the book is also at rest, so the net force on the book is zero.
Therefore:
Gravitational force acts downward and normal force from the lift floor acts upward.
The book is inside a lift.
The lift is at rest on the 5th floor.
The book is also at rest relative to the lift.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The floor of the lift exerts an equal and opposite normal force upward on the book.
Since the lift is at rest, the book is also at rest, so the net force on the book is zero.
Therefore:
Gravitational force acts downward and normal force from the lift floor acts upward.
6
A book is inside a helicopter, and the helicopter is hovering at rest in the air. What are the forces acting on the book?
Practice
A
Only gravitational force acts on the book.
B
Only the upward force from the helicopter acts on the book.
C
Gravitational force acts downward and an upward force from the helicopter acts on the book.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
C
(Gravitational force acts downward and an upward force from the helicopter acts on the book.)
š” Explanation
Given:
The book is inside a helicopter.
The helicopter is hovering at rest in the air.
Therefore, the book is also at rest relative to the helicopter.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The helicopter provides an upward force on the book to support it.
Since the helicopter and book remain at rest, these forces balance each other and the net force is zero.
Therefore:
Gravitational force acts downward and an upward force from the helicopter acts on the book.
The book is inside a helicopter.
The helicopter is hovering at rest in the air.
Therefore, the book is also at rest relative to the helicopter.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The helicopter provides an upward force on the book to support it.
Since the helicopter and book remain at rest, these forces balance each other and the net force is zero.
Therefore:
Gravitational force acts downward and an upward force from the helicopter acts on the book.
7
A book is hanging at rest from a thread. What are the forces acting on the book?
Practice
A
Only gravitational force acts on the book.
B
Only tension force acts on the book.
C
Gravitational force acts downward and tension force from the thread acts upward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
C
(Gravitational force acts downward and tension force from the thread acts upward.)
š” Explanation
Given:
The book is hanging at rest from a thread.
The book is not moving.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The thread exerts a tension force upward on the book.
Since the book is at rest, these forces balance each other and the net force is zero.
Therefore:
Gravitational force acts downward and tension force from the thread acts upward.
The book is hanging at rest from a thread.
The book is not moving.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest when the net external force acting on it is zero.
The Earth exerts a gravitational force downward on the book.
The thread exerts a tension force upward on the book.
Since the book is at rest, these forces balance each other and the net force is zero.
Therefore:
Gravitational force acts downward and tension force from the thread acts upward.
8
A book is falling freely from the 5th floor. If air resistance is neglected, what force acts on the book?
Practice
A
Only gravitational force acts downward on the book.
B
Only air resistance acts upward on the book.
C
Gravitational force acts downward and normal force acts upward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
A
(Only gravitational force acts downward on the book.)
š” Explanation
Given:
The book is falling freely from the 5th floor.
Air resistance is neglected.
The book is not in contact with any surface or support.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force produces acceleration in an object.
The Earth exerts a gravitational force downward on the falling book.
Since air resistance is neglected and the book is not supported by any surface, there is no upward force balancing gravity.
Therefore, gravity is the unbalanced force acting on the book, causing it to accelerate downward.
Therefore:
Only gravitational force acts downward on the book.
The book is falling freely from the 5th floor.
Air resistance is neglected.
The book is not in contact with any surface or support.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force produces acceleration in an object.
The Earth exerts a gravitational force downward on the falling book.
Since air resistance is neglected and the book is not supported by any surface, there is no upward force balancing gravity.
Therefore, gravity is the unbalanced force acting on the book, causing it to accelerate downward.
Therefore:
Only gravitational force acts downward on the book.
9
A force is applied to a book on a horizontal surface. The book moves some distance and then stops after the applied force is removed. What forces act on the book while it is moving?
Practice
A
Only the applied force acts on the book.
B
Gravitational force acts downward, normal force acts upward, and frictional force acts opposite to the motion.
C
Gravitational force acts upward and frictional force acts downward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
B
(Gravitational force acts downward, normal force acts upward, and frictional force acts opposite to the motion.)
š” Explanation
Given:
The book is on a horizontal surface.
A force is applied to the book, causing it to move.
After the applied force is removed, the book moves some distance and stops.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force causes an object to accelerate or decelerate.
The Earth exerts a gravitational force downward on the book.
The horizontal surface exerts a normal force upward on the book.
Friction acts opposite to the direction of motion and slows the book down after the applied force is removed.
The frictional force produces a net force opposite to the motion, causing the book to decelerate and eventually stop.
Therefore:
Gravitational force acts downward, normal force acts upward, and frictional force acts opposite to the motion.
The book is on a horizontal surface.
A force is applied to the book, causing it to move.
After the applied force is removed, the book moves some distance and stops.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force causes an object to accelerate or decelerate.
The Earth exerts a gravitational force downward on the book.
The horizontal surface exerts a normal force upward on the book.
Friction acts opposite to the direction of motion and slows the book down after the applied force is removed.
The frictional force produces a net force opposite to the motion, causing the book to decelerate and eventually stop.
Therefore:
Gravitational force acts downward, normal force acts upward, and frictional force acts opposite to the motion.
10
A train is moving with uniform velocity on a straight horizontal track. A book is resting on the horizontal surface of a seat inside the train. What are the forces acting on the train and the book?
Practice
A
The train and book both have a net force in the direction of motion.
B
The book has only gravitational force, while the train has no force acting on it.
C
On the book, gravitational force acts downward and normal force acts upward; the train has forces acting on it that balance so its net force is zero.
D
No forces act on either the train or the book.
ā Show Answer
ā Correct Answer:
C
(On the book, gravitational force acts downward and normal force acts upward; the train has forces acting on it that balance so its net force is zero.)
š” Explanation
Given:
The train is moving with uniform velocity in a straight line.
The book is resting on the surface of the train seat relative to the train.
Therefore, both the train and the book have zero acceleration.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object continues in its state of rest or uniform motion when the net external force acting on it is zero.
For the book:
The Earth exerts a gravitational force downward on the book.
The seat exerts an equal normal force upward on the book.
These forces balance, so the net force on the book is zero.
For the train:
The train is moving with uniform velocity, so its acceleration is zero.
Therefore, the net external force on the train is zero.
There can be several forces acting on the train, but they balance each other overall.
Therefore:
On the book, gravitational force acts downward and normal force acts upward; the train has forces acting on it that balance so its net force is zero.
The train is moving with uniform velocity in a straight line.
The book is resting on the surface of the train seat relative to the train.
Therefore, both the train and the book have zero acceleration.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object continues in its state of rest or uniform motion when the net external force acting on it is zero.
For the book:
The Earth exerts a gravitational force downward on the book.
The seat exerts an equal normal force upward on the book.
These forces balance, so the net force on the book is zero.
For the train:
The train is moving with uniform velocity, so its acceleration is zero.
Therefore, the net external force on the train is zero.
There can be several forces acting on the train, but they balance each other overall.
Therefore:
On the book, gravitational force acts downward and normal force acts upward; the train has forces acting on it that balance so its net force is zero.
11
A train is moving non-uniformly on a horizontal track, and a book is resting on the horizontal surface of a seat inside the train. What are the forces acting on the train and the book?
Practice
A
The train and book both have zero net force because they are moving.
B
The book has only gravitational force, while the train has no net force.
C
The book has gravitational force downward, normal force upward, and a horizontal force from the seat that accelerates it with the train; the train has a non-zero net external force.
D
No forces act on either the train or the book.
ā Show Answer
ā Correct Answer:
C
(The book has gravitational force downward, normal force upward, and a horizontal force from the seat that accelerates it with the train; the train has a non-zero net external force.)
š” Explanation
Given:
The train is moving non-uniformly, so its velocity is changing.
Therefore, the train has acceleration.
The book is resting on the seat relative to the train, so the book accelerates along with the train.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that a net external force produces acceleration.
Since the train is accelerating, a non-zero net external force acts on the train.
For the book:
The Earth exerts a gravitational force downward.
The seat exerts a normal force upward.
The seat also exerts a horizontal frictional force on the book, which causes the book to accelerate along with the train.
Therefore:
The book has gravitational force downward, normal force upward, and a horizontal force from the seat that accelerates it with the train; the train has a non-zero net external force.
The train is moving non-uniformly, so its velocity is changing.
Therefore, the train has acceleration.
The book is resting on the seat relative to the train, so the book accelerates along with the train.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that a net external force produces acceleration.
Since the train is accelerating, a non-zero net external force acts on the train.
For the book:
The Earth exerts a gravitational force downward.
The seat exerts a normal force upward.
The seat also exerts a horizontal frictional force on the book, which causes the book to accelerate along with the train.
Therefore:
The book has gravitational force downward, normal force upward, and a horizontal force from the seat that accelerates it with the train; the train has a non-zero net external force.
12
A train is accelerating forward, and a book placed on the horizontal seat slips backward relative to the train. What are the forces acting on the book?
Practice
A
Only gravitational force acts on the book.
B
Gravitational force acts downward, normal force acts upward, and frictional force acts forward on the book.
C
Gravitational force acts downward and frictional force acts backward on the book.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
B
(Gravitational force acts downward, normal force acts upward, and frictional force acts forward on the book.)
š” Explanation
Given:
The train is accelerating forward.
The book slips backward relative to the train.
The book is in contact with the horizontal seat.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that a net external force produces acceleration.
The Earth exerts a gravitational force downward on the book.
The seat exerts a normal force upward on the book.
Since the train is accelerating forward, the seat tends to move forward relative to the book.
Friction acts between the book and the seat in the forward direction, trying to prevent the relative slipping.
If the frictional force is not sufficient to accelerate the book along with the train, the book slips backward relative to the train.
Therefore:
Gravitational force acts downward, normal force acts upward, and frictional force acts forward on the book.
The train is accelerating forward.
The book slips backward relative to the train.
The book is in contact with the horizontal seat.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that a net external force produces acceleration.
The Earth exerts a gravitational force downward on the book.
The seat exerts a normal force upward on the book.
Since the train is accelerating forward, the seat tends to move forward relative to the book.
Friction acts between the book and the seat in the forward direction, trying to prevent the relative slipping.
If the frictional force is not sufficient to accelerate the book along with the train, the book slips backward relative to the train.
Therefore:
Gravitational force acts downward, normal force acts upward, and frictional force acts forward on the book.
13
A book is dropped from a moving train and falls outside the train toward the Earth's surface. If air resistance is neglected, what forces act on the book while it is falling?
Practice
A
Only gravitational force acts downward on the book.
B
Gravitational force acts downward and the force of the train acts forward on the book.
C
Gravitational force acts downward and normal force acts upward.
D
No force acts on the book.
ā Show Answer
ā Correct Answer:
A
(Only gravitational force acts downward on the book.)
š” Explanation
Given:
The book is dropped from a moving train.
The book is outside the train and is falling toward the Earth's surface.
The book is no longer in contact with the train.
Air resistance is neglected.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force produces acceleration.
After the book is released, the train no longer exerts a force on the book.
The Earth exerts gravitational force downward on the book.
There is no normal force because the book is not in contact with a surface.
The book continues to have the horizontal velocity it had when it was released, but this velocity is not a force.
Therefore:
Only gravitational force acts downward on the book.
The book is dropped from a moving train.
The book is outside the train and is falling toward the Earth's surface.
The book is no longer in contact with the train.
Air resistance is neglected.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force produces acceleration.
After the book is released, the train no longer exerts a force on the book.
The Earth exerts gravitational force downward on the book.
There is no normal force because the book is not in contact with a surface.
The book continues to have the horizontal velocity it had when it was released, but this velocity is not a force.
Therefore:
Only gravitational force acts downward on the book.
14
A ball is thrown into the air. After the ball leaves the hand, and if air resistance is neglected, what force acts on the ball?
Practice
A
Only gravitational force acts downward on the ball.
B
The throwing force continues to act forward on the ball.
C
Gravitational force acts downward and the throwing force acts forward on the ball.
D
No force acts on the ball.
ā Show Answer
ā Correct Answer:
A
(Only gravitational force acts downward on the ball.)
š” Explanation
Given:
The ball is thrown into the air.
The ball has already left the hand.
Air resistance is neglected.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force produces acceleration.
While the ball is in contact with the hand, the hand exerts a force on the ball and accelerates it.
After the ball leaves the hand, the hand no longer exerts a force on it.
The Earth continues to exert gravitational force downward on the ball.
The forward motion of the ball is due to the velocity it already has; velocity is not a force.
Therefore:
Only gravitational force acts downward on the ball.
The ball is thrown into the air.
The ball has already left the hand.
Air resistance is neglected.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced external force produces acceleration.
While the ball is in contact with the hand, the hand exerts a force on the ball and accelerates it.
After the ball leaves the hand, the hand no longer exerts a force on it.
The Earth continues to exert gravitational force downward on the ball.
The forward motion of the ball is due to the velocity it already has; velocity is not a force.
Therefore:
Only gravitational force acts downward on the ball.
15
A ball is thrown toward a wall. It hits the wall and comes back. What forces act on the ball while it is in contact with the wall?
Practice
A
Only gravitational force acts on the ball.
B
Only the force from the wall acts on the ball.
C
Gravitational force acts downward and the wall exerts a force on the ball away from the wall.
D
The throwing force continues to act on the ball and pushes it away from the wall.
ā Show Answer
ā Correct Answer:
C
(Gravitational force acts downward and the wall exerts a force on the ball away from the wall.)
š” Explanation
Given:
The ball is moving toward the wall.
The ball hits the wall and comes back.
The ball is in contact with the wall during the collision.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced force produces acceleration or a change in velocity.
During the collision, the wall exerts a force on the ball away from the wall.
This force changes the velocity of the ball and makes it move back in the opposite direction.
The Earth also exerts gravitational force downward on the ball.
Therefore:
Gravitational force acts downward and the wall exerts a force on the ball away from the wall.
The ball is moving toward the wall.
The ball hits the wall and comes back.
The ball is in contact with the wall during the collision.
Law applied: Newton's Second Law of Motion.
Why:
Newton's Second Law states that an unbalanced force produces acceleration or a change in velocity.
During the collision, the wall exerts a force on the ball away from the wall.
This force changes the velocity of the ball and makes it move back in the opposite direction.
The Earth also exerts gravitational force downward on the ball.
Therefore:
Gravitational force acts downward and the wall exerts a force on the ball away from the wall.
16
A 1 kg book is floating in space, and there are no planets or stars nearby. What is the net force acting on the book?
Practice
A
0 N
B
1 N
C
9.8 N
D
10 N
ā Show Answer
ā Correct Answer:
A
(0 N)
š” Explanation
Given:
Mass of the book = 1 kg
The book is in space.
There are no planets or stars nearby.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest or continues with uniform velocity when no unbalanced external force acts on it.
Since there are no planets or stars nearby, no significant gravitational force acts on the book.
No other external force is acting on the book.
Therefore:
Net force on the book = 0 N.
Mass of the book = 1 kg
The book is in space.
There are no planets or stars nearby.
Law applied: Newton's First Law of Motion.
Why:
Newton's First Law states that an object remains at rest or continues with uniform velocity when no unbalanced external force acts on it.
Since there are no planets or stars nearby, no significant gravitational force acts on the book.
No other external force is acting on the book.
Therefore:
Net force on the book = 0 N.
17
A 1 kg book is lying at rest on a horizontal surface on Earth. What is the net force acting on the book?
Practice
A
0 N
B
1 N
C
9.8 N
D
19.6 N
ā Show Answer
ā Correct Answer:
A
(0 N)
š” Explanation
Given:
Mass of the book = 1 kg
The book is at rest on a horizontal surface on Earth.
Law applied: Newton's First Law of Motion.
Why:
The Earth's gravitational force acts downward on the book.
The surface exerts an equal normal force upward on the book.
Therefore, the upward normal force and downward gravitational force balance each other.
Since the book is at rest, its acceleration is zero and the net force is zero.
Therefore:
Net force on the book = 0 N.
Mass of the book = 1 kg
The book is at rest on a horizontal surface on Earth.
Law applied: Newton's First Law of Motion.
Why:
The Earth's gravitational force acts downward on the book.
The surface exerts an equal normal force upward on the book.
Therefore, the upward normal force and downward gravitational force balance each other.
Since the book is at rest, its acceleration is zero and the net force is zero.
Therefore:
Net force on the book = 0 N.
18
A 1 kg book is on a horizontal surface on Earth. A force of 10 N is applied to the book in the +x direction. If friction is neglected, what is the net force acting on the book?
Practice
A
0 N
B
10 N in the +x direction
C
9.8 N in the +y direction
D
19.8 N in the +x direction
ā Show Answer
ā Correct Answer:
B
(10 N in the +x direction)
š” Explanation
Given:
Mass of the book = 1 kg
Applied force = 10 N in the +x direction
Friction is neglected.
The book is on a horizontal surface on Earth.
Law applied: Newton's Second Law of Motion.
Why:
The gravitational force acts downward with a weight of 9.8 N.
The normal force from the surface acts upward with a force of 9.8 N.
Therefore, the vertical forces balance each other and their net force is zero in the y-direction.
The applied force of 10 N acts in the +x direction.
Since friction is neglected, there is no force opposing the applied force in the x-direction.
Therefore:
Net force in the x-direction = 10 N.
Net force in the y-direction = 0 N.
Net force on the book = 10 N in the +x direction.
Mass of the book = 1 kg
Applied force = 10 N in the +x direction
Friction is neglected.
The book is on a horizontal surface on Earth.
Law applied: Newton's Second Law of Motion.
Why:
The gravitational force acts downward with a weight of 9.8 N.
The normal force from the surface acts upward with a force of 9.8 N.
Therefore, the vertical forces balance each other and their net force is zero in the y-direction.
The applied force of 10 N acts in the +x direction.
Since friction is neglected, there is no force opposing the applied force in the x-direction.
Therefore:
Net force in the x-direction = 10 N.
Net force in the y-direction = 0 N.
Net force on the book = 10 N in the +x direction.
19
A 1 kg book is on a horizontal surface on Earth. A force of 10 N is applied to the book in the +y direction. What is the net force acting on the book?
Practice
A
0 N
B
0.2 N in the +y direction
C
10 N in the +y direction
D
19.8 N in the +y direction
ā Show Answer
ā Correct Answer:
B
(0.2 N in the +y direction)
š” Explanation
Given:
Mass of the book = 1 kg
Applied force = 10 N in the +y direction
Weight of the book = 9.8 N downward
The book is initially on a horizontal surface.
Law applied: Newton's Second Law of Motion.
Why:
The applied force acts upward with 10 N.
The weight of the book acts downward with 9.8 N.
If the book remains in contact with the surface, the normal force cannot be negative. Since the upward applied force is greater than the weight, the book loses contact with the surface.
Therefore, the normal force becomes zero.
Net force in the y-direction:
F_net = 10 N - 9.8 N
F_net = 0.2 N upward
Therefore:
Net force on the book = 0.2 N in the +y direction.
Mass of the book = 1 kg
Applied force = 10 N in the +y direction
Weight of the book = 9.8 N downward
The book is initially on a horizontal surface.
Law applied: Newton's Second Law of Motion.
Why:
The applied force acts upward with 10 N.
The weight of the book acts downward with 9.8 N.
If the book remains in contact with the surface, the normal force cannot be negative. Since the upward applied force is greater than the weight, the book loses contact with the surface.
Therefore, the normal force becomes zero.
Net force in the y-direction:
F_net = 10 N - 9.8 N
F_net = 0.2 N upward
Therefore:
Net force on the book = 0.2 N in the +y direction.
20
A 1 kg book is on a horizontal surface on Earth. A force of 10 N is applied to the book in the +y direction. What is the net force, F_net, acting on the book?
Practice
A
0 N
B
0.2 N in the +y direction
C
10 N in the +y direction
D
20 N in the +y direction
ā Show Answer
ā Correct Answer:
A
(0 N)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force, F = 10 N upward (+y direction)
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Why:
Weight of the book, W = mg
W = 1 Ć 10
W = 10 N downward
Forces acting on the book:
Applied force = 10 N upward
Weight = 10 N downward
Normal force = 0 N
Since the applied upward force is equal to the weight, the book is just losing contact with the horizontal surface.
Therefore, the normal force from the surface is zero.
Therefore:
F_net = 10 N - 10 N + 0 N
F_net = 0 N.
Mass of the book, m = 1 kg
Applied force, F = 10 N upward (+y direction)
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Why:
Weight of the book, W = mg
W = 1 Ć 10
W = 10 N downward
Forces acting on the book:
Applied force = 10 N upward
Weight = 10 N downward
Normal force = 0 N
Since the applied upward force is equal to the weight, the book is just losing contact with the horizontal surface.
Therefore, the normal force from the surface is zero.
Therefore:
F_net = 10 N - 10 N + 0 N
F_net = 0 N.
21
A 1 kg book is on a horizontal surface on Earth. A force of 20 N is applied to the book in the +y direction. What is the net force, F_net, acting on the book?
Practice
A
0 N
B
10 N in the +y direction
C
20 N in the +y direction
D
30 N in the +y direction
ā Show Answer
ā Correct Answer:
B
(10 N in the +y direction)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force, F = 20 N upward (+y direction)
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 20 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = 0 N
Why:
The applied upward force of 20 N is greater than the weight of 10 N.
Therefore, the book loses contact with the horizontal surface, so the normal force becomes zero.
Therefore:
F_net = 20 N + 0 N - 10 N
F_net = 10 N upward.
The acceleration of the book is:
a = F_net / m
a = 10 / 1
a = 10 m/sĀ² upward.
Mass of the book, m = 1 kg
Applied force, F = 20 N upward (+y direction)
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 20 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = 0 N
Why:
The applied upward force of 20 N is greater than the weight of 10 N.
Therefore, the book loses contact with the horizontal surface, so the normal force becomes zero.
Therefore:
F_net = 20 N + 0 N - 10 N
F_net = 10 N upward.
The acceleration of the book is:
a = F_net / m
a = 10 / 1
a = 10 m/sĀ² upward.
22
A 1 kg book is on a horizontal surface on Earth. A force of 20 N is applied to the book in the +x direction. A frictional force of 10 N acts in the -x direction. What is the net force, F_net, acting on the book?
Practice
A
10 N in the +x direction
B
10 N in the -x direction
C
30 N in the +x direction
D
0 N
ā Show Answer
ā Correct Answer:
A
(10 N in the +x direction)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = 10 N upward
Why:
The weight and normal force are equal and opposite, so the net force in the y-direction is zero.
In the x-direction, the applied force is 20 N and frictional force is 10 N in the opposite direction.
Therefore:
F_net = 20 N - 10 N
F_net = 10 N in the +x direction.
Therefore:
F_net = 10 N in the +x direction.
Mass of the book, m = 1 kg
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = 10 N upward
Why:
The weight and normal force are equal and opposite, so the net force in the y-direction is zero.
In the x-direction, the applied force is 20 N and frictional force is 10 N in the opposite direction.
Therefore:
F_net = 20 N - 10 N
F_net = 10 N in the +x direction.
Therefore:
F_net = 10 N in the +x direction.
23
A 1 kg book is on a horizontal surface on Earth. A force of 20 N is applied in the +x direction, a frictional force of 10 N acts in the -x direction, and another force of 20 N is applied in the +y direction. Taking g = 10 m/sĀ², what is the magnitude and direction of F_net?
Practice
A
10 N, in the +x direction
B
10ā2 N (ā14.14 N), at 45Ā° above the +x direction
C
20 N, in the +y direction
D
30 N, at 45Ā° above the +x direction
ā Show Answer
ā Correct Answer:
B
(10ā2 N (ā14.14 N), at 45Ā° above the +x direction)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Weight = mg = 1 Ć 10 = 10 N in the -y direction
Normal force = 0 N because the upward applied force is greater than the weight, so the book loses contact with the surface.
Net force in the x-direction:
F_net,x = 20 - 10
F_net,x = 10 N
Net force in the y-direction:
F_net,y = 20 - 10
F_net,y = 10 N
Magnitude of net force:
F_net = ā(F_net,xĀ² + F_net,yĀ²)
F_net = ā(10Ā² + 10Ā²)
F_net = 10ā2 N ā 14.14 N
Direction:
tan(Īø) = F_net,y / F_net,x
tan(Īø) = 10 / 10 = 1
Īø = 45Ā°
Therefore:
F_net = 10ā2 N ā 14.14 N, at 45Ā° above the +x direction.
Mass of the book, m = 1 kg
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 20 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Weight = mg = 1 Ć 10 = 10 N in the -y direction
Normal force = 0 N because the upward applied force is greater than the weight, so the book loses contact with the surface.
Net force in the x-direction:
F_net,x = 20 - 10
F_net,x = 10 N
Net force in the y-direction:
F_net,y = 20 - 10
F_net,y = 10 N
Magnitude of net force:
F_net = ā(F_net,xĀ² + F_net,yĀ²)
F_net = ā(10Ā² + 10Ā²)
F_net = 10ā2 N ā 14.14 N
Direction:
tan(Īø) = F_net,y / F_net,x
tan(Īø) = 10 / 10 = 1
Īø = 45Ā°
Therefore:
F_net = 10ā2 N ā 14.14 N, at 45Ā° above the +x direction.
24
A 1 kg book is on a horizontal surface on Earth. A force of 40 N is applied in the +x direction, a frictional force of 10 N acts in the -x direction, and another force of 20 N is applied in the +y direction. Taking g = 10 m/sĀ², what is the magnitude and direction of F_net?
Practice
A
30 N at 18.4Ā° above the +x direction
B
30ā2 N at 45Ā° above the +x direction
C
10ā10 N at 45Ā° above the +x direction
D
50 N in the +x direction
ā Show Answer
ā Correct Answer:
A
(30 N at 18.4Ā° above the +x direction)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 40 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 40 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Weight = mg = 1 Ć 10 = 10 N in the -y direction
Normal force = 0 N because the upward applied force is greater than the weight, so the book loses contact with the surface.
Net force in the x-direction:
F_net,x = 40 - 10
F_net,x = 30 N
Net force in the y-direction:
F_net,y = 20 - 10
F_net,y = 10 N
Magnitude of net force:
F_net = ā(F_net,xĀ² + F_net,yĀ²)
F_net = ā(30Ā² + 10Ā²)
F_net = ā1000
F_net = 10ā10 N ā 31.62 N
Direction:
tan(Īø) = F_net,y / F_net,x
tan(Īø) = 10 / 30 = 1/3
Īø ā 18.4Ā°
Therefore:
F_net = 10ā10 N ā 31.62 N, at 18.4Ā° above the +x direction.
Mass of the book, m = 1 kg
Applied force = 40 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 40 N in the +x direction
Frictional force = 10 N in the -x direction
Applied force = 20 N in the +y direction
Weight = mg = 1 Ć 10 = 10 N in the -y direction
Normal force = 0 N because the upward applied force is greater than the weight, so the book loses contact with the surface.
Net force in the x-direction:
F_net,x = 40 - 10
F_net,x = 30 N
Net force in the y-direction:
F_net,y = 20 - 10
F_net,y = 10 N
Magnitude of net force:
F_net = ā(F_net,xĀ² + F_net,yĀ²)
F_net = ā(30Ā² + 10Ā²)
F_net = ā1000
F_net = 10ā10 N ā 31.62 N
Direction:
tan(Īø) = F_net,y / F_net,x
tan(Īø) = 10 / 30 = 1/3
Īø ā 18.4Ā°
Therefore:
F_net = 10ā10 N ā 31.62 N, at 18.4Ā° above the +x direction.
25
A 1 kg book is hanging at rest from the ceiling by a vertical thread. Taking g = 10 m/sĀ², what is the tension force in the thread and the net force, F_net, acting on the book?
Practice
A
T = 10 N upward, F_net = 0 N
B
T = 0 N, F_net = 10 N downward
C
T = 10 N downward, F_net = 0 N
D
T = 20 N upward, F_net = 10 N upward
ā Show Answer
ā Correct Answer:
A
(T = 10 N upward, F_net = 0 N)
š” Explanation
Given:
Mass of the book, m = 1 kg
Acceleration due to gravity, g = 10 m/sĀ²
The book is hanging at rest.
Law applied: Newton's First Law of Motion.
Forces acting on the book:
Weight = mg = 1 Ć 10 = 10 N downward
Tension = T upward
Why:
The book is at rest, so its acceleration is zero.
According to Newton's First Law, the net force must therefore be zero.
Hence, the upward tension must balance the downward weight.
Therefore:
T = 10 N upward
F_net = T - W
F_net = 10 - 10
F_net = 0 N.
Mass of the book, m = 1 kg
Acceleration due to gravity, g = 10 m/sĀ²
The book is hanging at rest.
Law applied: Newton's First Law of Motion.
Forces acting on the book:
Weight = mg = 1 Ć 10 = 10 N downward
Tension = T upward
Why:
The book is at rest, so its acceleration is zero.
According to Newton's First Law, the net force must therefore be zero.
Hence, the upward tension must balance the downward weight.
Therefore:
T = 10 N upward
F_net = T - W
F_net = 10 - 10
F_net = 0 N.
26
A 1 kg book is hanging from a ceiling by a thread. The tension force in the thread is 40 N upward. Taking g = 10 m/sĀ², what is the net force, F_net, acting on the book?
Practice
A
0 N
B
10 N downward
C
30 N upward
D
40 N upward
ā Show Answer
ā Correct Answer:
C
(30 N upward)
š” Explanation
Given:
Mass of the book, m = 1 kg
Tension force, T = 40 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Tension = 40 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Why:
The tension force is greater than the weight of the book.
Therefore, the forces do not balance and there is a net force upward.
Therefore:
F_net = T - W
F_net = 40 - 10
F_net = 30 N upward.
Mass of the book, m = 1 kg
Tension force, T = 40 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Tension = 40 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Why:
The tension force is greater than the weight of the book.
Therefore, the forces do not balance and there is a net force upward.
Therefore:
F_net = T - W
F_net = 40 - 10
F_net = 30 N upward.
27
A 1 kg ball is thrown vertically upward with an applied force of 20 N. After the ball leaves the hand, what is its apparent weight? Take g = 10 m/sĀ² and neglect air resistance.
Practice
A
0 N
B
10 N
C
20 N
D
30 N
ā Show Answer
ā Correct Answer:
A
(0 N)
š” Explanation
Given:
Mass of the ball, m = 1 kg
Applied force used to throw the ball = 20 N
Acceleration due to gravity, g = 10 m/sĀ²
The ball has left the hand.
Air resistance is neglected.
Law applied: Newton's Second Law of Motion.
Why:
While the ball is in contact with the hand, the hand exerts an upward force on the ball.
After the ball leaves the hand, the hand no longer exerts any force on the ball.
The 20 N throwing force does not continue acting after the ball leaves the hand.
The ball continues upward because it has acquired upward velocity; gravity then acts downward.
The only force acting on the ball after release is its weight.
Weight, W = mg = 1 Ć 10 = 10 N downward.
Since the ball is not in contact with any surface or support, there is no normal or tension force.
Apparent weight:
Apparent weight is the contact force acting on the object.
Since no contact force acts on the ball after it is released:
Apparent weight = 0 N.
Therefore:
Apparent weight = 0 N.
Mass of the ball, m = 1 kg
Applied force used to throw the ball = 20 N
Acceleration due to gravity, g = 10 m/sĀ²
The ball has left the hand.
Air resistance is neglected.
Law applied: Newton's Second Law of Motion.
Why:
While the ball is in contact with the hand, the hand exerts an upward force on the ball.
After the ball leaves the hand, the hand no longer exerts any force on the ball.
The 20 N throwing force does not continue acting after the ball leaves the hand.
The ball continues upward because it has acquired upward velocity; gravity then acts downward.
The only force acting on the ball after release is its weight.
Weight, W = mg = 1 Ć 10 = 10 N downward.
Since the ball is not in contact with any surface or support, there is no normal or tension force.
Apparent weight:
Apparent weight is the contact force acting on the object.
Since no contact force acts on the ball after it is released:
Apparent weight = 0 N.
Therefore:
Apparent weight = 0 N.
28
A lift is moving upward with an acceleration of 2 m/sĀ². A man of mass 100 kg is standing inside the lift. How much apparent weight, in kg, does the man feel? Take g = 10 m/sĀ².
Practice
A
80 kg
B
100 kg
C
120 kg
D
200 kg
ā Show Answer
ā Correct Answer:
C
(120 kg)
š” Explanation
Given:
Mass of the man, m = 100 kg
Acceleration of the lift, a = 2 m/sĀ² upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the man:
Normal force, N, acts upward.
Weight, W = mg, acts downward.
Since the lift accelerates upward, the normal force is greater than the weight.
Using Newton's Second Law:
N - mg = ma
N = m(g + a)
N = 100(10 + 2)
N = 1200 N
Apparent weight in kg:
m_apparent = N / g
m_apparent = 1200 / 10
m_apparent = 120 kg
Therefore:
The man feels an apparent weight of 120 kg.
Mass of the man, m = 100 kg
Acceleration of the lift, a = 2 m/sĀ² upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the man:
Normal force, N, acts upward.
Weight, W = mg, acts downward.
Since the lift accelerates upward, the normal force is greater than the weight.
Using Newton's Second Law:
N - mg = ma
N = m(g + a)
N = 100(10 + 2)
N = 1200 N
Apparent weight in kg:
m_apparent = N / g
m_apparent = 1200 / 10
m_apparent = 120 kg
Therefore:
The man feels an apparent weight of 120 kg.
29
A lift is moving upward with a constant speed of 2 m/s. A man of mass 100 kg is standing inside the lift. How much apparent weight, in kg, does the man feel? Take g = 10 m/sĀ².
Practice
A
80 kg
B
100 kg
C
120 kg
D
200 kg
ā Show Answer
ā Correct Answer:
B
(100 kg)
š” Explanation
Given:
Mass of the man, m = 100 kg
Velocity of the lift = 2 m/s upward
The lift is moving with constant velocity.
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's First Law of Motion.
Why:
The lift is moving with constant velocity, so its acceleration is zero.
Therefore, the man also has zero acceleration.
The forces acting on the man are weight downward and normal force upward.
Since acceleration is zero, these forces balance each other.
Weight:
W = mg
W = 100 Ć 10
W = 1000 N downward
Therefore:
Normal force, N = 1000 N upward.
Apparent weight = N / g
Apparent weight = 1000 / 10
Apparent weight = 100 kg.
Therefore:
The man feels an apparent weight of 100 kg.
Mass of the man, m = 100 kg
Velocity of the lift = 2 m/s upward
The lift is moving with constant velocity.
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's First Law of Motion.
Why:
The lift is moving with constant velocity, so its acceleration is zero.
Therefore, the man also has zero acceleration.
The forces acting on the man are weight downward and normal force upward.
Since acceleration is zero, these forces balance each other.
Weight:
W = mg
W = 100 Ć 10
W = 1000 N downward
Therefore:
Normal force, N = 1000 N upward.
Apparent weight = N / g
Apparent weight = 1000 / 10
Apparent weight = 100 kg.
Therefore:
The man feels an apparent weight of 100 kg.
30
A lift is moving downward with an acceleration of 2 m/sĀ². A man of mass 100 kg is standing inside the lift. How much apparent weight, in kg, does the man feel? Take g = 10 m/sĀ².
Practice
A
80 kg
B
100 kg
C
120 kg
D
200 kg
ā Show Answer
ā Correct Answer:
A
(80 kg)
š” Explanation
Given:
Mass of the man, m = 100 kg
Acceleration of the lift, a = 2 m/sĀ² downward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the man:
Weight, W = mg, acts downward.
Normal force, N, acts upward.
Why:
The lift accelerates downward, so the man also has a downward acceleration.
Taking upward as positive, the acceleration is a = -2 m/sĀ².
Using Newton's Second Law:
N - mg = ma
N - 100 Ć 10 = 100 Ć (-2)
N - 1000 = -200
N = 800 N
Apparent weight in kg:
m_apparent = N / g
m_apparent = 800 / 10
m_apparent = 80 kg
Therefore:
The man feels an apparent weight of 80 kg.
Mass of the man, m = 100 kg
Acceleration of the lift, a = 2 m/sĀ² downward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the man:
Weight, W = mg, acts downward.
Normal force, N, acts upward.
Why:
The lift accelerates downward, so the man also has a downward acceleration.
Taking upward as positive, the acceleration is a = -2 m/sĀ².
Using Newton's Second Law:
N - mg = ma
N - 100 Ć 10 = 100 Ć (-2)
N - 1000 = -200
N = 800 N
Apparent weight in kg:
m_apparent = N / g
m_apparent = 800 / 10
m_apparent = 80 kg
Therefore:
The man feels an apparent weight of 80 kg.
31
A lift is moving downward with a constant speed of 2 m/s. A man of mass 100 kg is standing inside the lift. How much apparent weight, in kg, does the man feel? Take g = 10 m/sĀ².
Practice
A
80 kg
B
100 kg
C
120 kg
D
200 kg
ā Show Answer
ā Correct Answer:
B
(100 kg)
š” Explanation
Given:
Mass of the man, m = 100 kg
Speed of the lift = 2 m/s downward
The lift is moving with constant speed.
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's First Law of Motion.
Why:
The lift is moving downward with constant speed, so its acceleration is zero.
Therefore, the man also has zero acceleration.
The forces acting on the man are weight downward and normal force upward.
Since acceleration is zero, these forces balance each other.
Weight:
W = mg
W = 100 Ć 10
W = 1000 N downward
Therefore:
Normal force, N = 1000 N upward.
Apparent weight = N / g
Apparent weight = 1000 / 10
Apparent weight = 100 kg.
Therefore:
The man feels an apparent weight of 100 kg.
Mass of the man, m = 100 kg
Speed of the lift = 2 m/s downward
The lift is moving with constant speed.
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's First Law of Motion.
Why:
The lift is moving downward with constant speed, so its acceleration is zero.
Therefore, the man also has zero acceleration.
The forces acting on the man are weight downward and normal force upward.
Since acceleration is zero, these forces balance each other.
Weight:
W = mg
W = 100 Ć 10
W = 1000 N downward
Therefore:
Normal force, N = 1000 N upward.
Apparent weight = N / g
Apparent weight = 1000 / 10
Apparent weight = 100 kg.
Therefore:
The man feels an apparent weight of 100 kg.
32
A 1 kg book is resting on a horizontal table on Earth. An upward force of 2 N is applied to the book. Taking g = 10 m/sĀ², what are the normal force and the net force, F_net, acting on the book?
Practice
A
Normal force = 8 N upward, F_net = 0 N
B
Normal force = 10 N upward, F_net = 2 N upward
C
Normal force = 8 N upward, F_net = 2 N upward
D
Normal force = 12 N upward, F_net = 0 N
ā Show Answer
ā Correct Answer:
A
(Normal force = 8 N upward, F_net = 0 N)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 2 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 2 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = N upward
Why:
The book remains in contact with the table because the upward applied force is less than its weight.
Since the book remains at rest on the table, its vertical acceleration is zero.
Therefore, the upward forces must balance the downward weight.
Using Newton's Second Law:
F_net = 0
N + 2 - 10 = 0
N = 8 N upward
Therefore:
Normal force = 8 N upward.
F_net = 0 N.
Mass of the book, m = 1 kg
Applied force = 2 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 2 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = N upward
Why:
The book remains in contact with the table because the upward applied force is less than its weight.
Since the book remains at rest on the table, its vertical acceleration is zero.
Therefore, the upward forces must balance the downward weight.
Using Newton's Second Law:
F_net = 0
N + 2 - 10 = 0
N = 8 N upward
Therefore:
Normal force = 8 N upward.
F_net = 0 N.
33
A 1 kg book is resting on a horizontal table on Earth. An upward force of 10 N is applied to the book. Taking g = 10 m/sĀ², what are the normal force and the net force, F_net, acting on the book?
Practice
A
Normal force = 0 N, F_net = 0 N
B
Normal force = 10 N upward, F_net = 0 N
C
Normal force = 0 N, F_net = 10 N upward
D
Normal force = 10 N upward, F_net = 10 N upward
ā Show Answer
ā Correct Answer:
A
(Normal force = 0 N, F_net = 0 N)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 10 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 10 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = N
Why:
The applied upward force is exactly equal to the weight of the book.
Therefore, the book is just losing contact with the table, so the normal force becomes zero.
Net force:
F_net = Applied force + Normal force - Weight
F_net = 10 + 0 - 10
F_net = 0 N
Therefore:
Normal force = 0 N.
F_net = 0 N.
Mass of the book, m = 1 kg
Applied force = 10 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 10 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = N
Why:
The applied upward force is exactly equal to the weight of the book.
Therefore, the book is just losing contact with the table, so the normal force becomes zero.
Net force:
F_net = Applied force + Normal force - Weight
F_net = 10 + 0 - 10
F_net = 0 N
Therefore:
Normal force = 0 N.
F_net = 0 N.
34
A 1 kg book is resting on a horizontal table on Earth. An upward force of 15 N is applied to the book. Taking g = 10 m/sĀ², what are the normal force and the net force, F_net, acting on the book?
Practice
A
Normal force = 0 N, F_net = 5 N upward
B
Normal force = 5 N upward, F_net = 0 N
C
Normal force = 10 N upward, F_net = 5 N upward
D
Normal force = 15 N upward, F_net = 5 N upward
ā Show Answer
ā Correct Answer:
A
(Normal force = 0 N, F_net = 5 N upward)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 15 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 15 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = 0 N
Why:
The applied upward force of 15 N is greater than the weight of 10 N.
Therefore, the book loses contact with the table.
Once the book loses contact with the table, the normal force becomes zero.
Therefore:
F_net = 15 N + 0 N - 10 N
F_net = 5 N upward.
Normal force = 0 N.
F_net = 5 N upward.
Mass of the book, m = 1 kg
Applied force = 15 N upward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 15 N upward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = 0 N
Why:
The applied upward force of 15 N is greater than the weight of 10 N.
Therefore, the book loses contact with the table.
Once the book loses contact with the table, the normal force becomes zero.
Therefore:
F_net = 15 N + 0 N - 10 N
F_net = 5 N upward.
Normal force = 0 N.
F_net = 5 N upward.
35
A 1 kg book is resting on a horizontal table on Earth. A downward force of 15 N is applied to the book. Taking g = 10 m/sĀ², what are the normal force and the net force, F_net, acting on the book?
Practice
A
Normal force = 10 N upward, F_net = 15 N downward
B
Normal force = 25 N upward, F_net = 0 N
C
Normal force = 15 N upward, F_net = 10 N downward
D
Normal force = 25 N upward, F_net = 0 N
ā Show Answer
ā Correct Answer:
B
(Normal force = 25 N upward, F_net = 0 N)
š” Explanation
Given:
Mass of the book, m = 1 kg
Applied force = 15 N downward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 15 N downward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = N upward
Why:
The book remains in contact with the table, so the table provides an upward normal force.
The two downward forces are the applied force and the weight.
Since the book remains at rest on the table, its vertical acceleration is zero.
Therefore, the normal force must balance both downward forces.
Using Newton's Second Law:
F_net = 0
N - 15 - 10 = 0
N = 25 N upward
Therefore:
Normal force = 25 N upward.
F_net = 0 N.
Mass of the book, m = 1 kg
Applied force = 15 N downward
Acceleration due to gravity, g = 10 m/sĀ²
Law applied: Newton's Second Law of Motion.
Forces acting on the book:
Applied force = 15 N downward
Weight = mg = 1 Ć 10 = 10 N downward
Normal force = N upward
Why:
The book remains in contact with the table, so the table provides an upward normal force.
The two downward forces are the applied force and the weight.
Since the book remains at rest on the table, its vertical acceleration is zero.
Therefore, the normal force must balance both downward forces.
Using Newton's Second Law:
F_net = 0
N - 15 - 10 = 0
N = 25 N upward
Therefore:
Normal force = 25 N upward.
F_net = 0 N.