# AP Physics 1 : Newton's Third Law

## Example Questions

### Example Question #1 : Newton's Third Law

A cat of mass 5kg jumps on a dining table of mass 30kg. As the cat walks around on the table, what is the average force that the table applies to the cat?

Explanation:

This question is testing your understanding of Newton's third law (equal and opposite forces). The forces between the cat and table depend solely on the mass of the cat; therefore, the mass of the table is irrelevant.

The force that the cat applies to the table is simply its weight. According to Newton's third law, the table also applies a force to the cat of the same magnitude. The force on the cat from the table is:

### Example Question #2 : Newton's Third Law

A 15 kg block and a 10 kg block are hanging on opposite sides of a pulley (see picture). Assuming a frictionless, massless pulley, determine the acceleration of the blocks once they are released from rest.

Explanation:

Since the two blocks are connected by the rope of the pulley, they will have the same acceleration and we can treat them as a single system. Start by drawing a free-body diagram including all the forces acting on each object.  Also, choose a direction to be considered the positive direction (+) and a direction to be the negative direction (-).

Each block has two forces acting on it: weight and tension. The weight of each block can be found using the equation:

Therefore, the weight of the 10 kg block is 100 N, and the weight of the 15 kg block is 150 N.

According to Newton's third law, for every force there is an equal and opposite force. The two tension forces, in this case, are an action/reaction pair; they are equal in magnitude but opposite in direction.

Now, using Newton's second law:

Since we are treating the system as a whole, or as if it is moving as a single object, we will add up all the forces acting on each object.

All forces which point in the positive (+) direction, as shown in the free body diagram above, will also be positive when put into the equation. All forces pointing in the negative (-) direction will also be negative in the equation.

What should we use for "" in the equation? Since we are treating the whole system as a single object, we must add all the masses together. In other words, 10 kg plus 15 kg, which is 25 kg total mass.

Notice now that the two tension forces will be canceled out, since they are action/reaction pairs and thus are equal but opposite in sign. So, solve for acceleration:

### Example Question #3 : Newton's Third Law

Dave is riding his skateboard and pushes off the ground with his foot. This causes him to accelerate at a rate of . Dave weighs 589 N. How strong was his push off the ground?

Explanation:

Dave weighs 589 N. This means his mass is

He accelerates at , which means he was pushed by a force of

By Newton's third law of motion, Dave must also have pushed of the ground with a force of 240 Newtons.

### Example Question #1 : Newton's Third Law

A man shoots a rifle and the force of the shot results in recoil. The magnitude of the force on the rifle __________ the magnitude of force on the bullet, and the magnitude of acceleration of the rile __________ that of the bullet.

equals . . . equals

is less than . . . is greater than

is greater than . . . is less than

equals . . . is less than

is less than . . . is less than

equals . . . is less than

Explanation:

Consistent with Newton's third law, which states that every force has an equal and opposite reaction, the force on the rifle is equal to the force on the bulet. However, the rifle has a larger mass, so the magnitude of its acceleration is less than that of the bullet.

### Example Question #301 : Forces

Two cars, one of mass 500kg and one of mass 250kg, collide head on. The car with more mass experiences a(n) __________ force and a(n) __________ acceleration with respect to the the smaller car.

larger . . . larger

larger . . . smaller

equal . . . smaller

equal . . . larger

equal . . . smaller

Explanation:

The cars will experience the same force, due to Newtown's third law. Because the larger car experiences the same force and has a larger mass, by Newton's first law, it will have a smaller acceleration.

### Example Question #1 : Newton's Third Law

A book exerts a force of 2N downwards, into a chair that exerts a force of 5N dowwards to the floor it stands on. What is the force that the floor exerts upwards on the chair?

Explanation:

By Newton's third law, for every reaction there is an equal and opposite reaction. The floor must exert a 7N force upwards on the chair for the system to remain at rest. If it exerted less than that, the chair would be accelerating into the floor. This force, exerted by a surface, perpendicular to it, is called the normal force.

### Example Question #7 : Newton's Third Law

A football player, feeling aggressive, is picking on a kid much smaller than himself. The football player asserts: "All of my hours in the weight room prove I can hit you harder than you hit me!" The smaller and more reserved gentleman replies: "Ya of course you can. I'm much weaker than you". Assuming by "hit" they mean "apply a force", are these two correct to think the football player can hit harder? Why?

No, Newton's third law says that the force two objects act on each other is always EQUAL in magnitude and opposite in direction.

No, Newton's first law says that the force two objects act on each other is always EQUAL in magnitude and opposite in direction.

Yes, Newton's second law says that the football player will cause the smaller gentleman to accelerate to a greater extent. Therefor he exterts a greater force.

Yes, Newton's second law says that football-playing-high-school bullies always hit harder.

No, Newton's third law says that the force two objects act on each other is always EQUAL in magnitude and opposite in direction.

Explanation:

The relative mass of two interacting objects does not influence the magnitude of the force that the two objects exert on each other. Newton's third laws states the force must be equal in magnitude. If you're trying to reconcile how a football player is unable to "hit harder" than someone who does not lift weights, the answer lies in Newton's second law.

The football player weighs more and thus experiences a small acceleration. The smaller gentleman experiences a large acceleration due to his relatively small mass. This large acceleration is what we view when we see a large football player hit someone smaller. The football player hardly changes his motion while the smaller person will fly backwards.

### Example Question #1 : Newton's Third Law

Describe the phenomenon of a seat belt keeping someone restrained in their seat during a car crash. In other words, why did the person not leave their seat?

All the laws describe why the person was not ejected from their seat

Newton's third law

Tension force law

Newton's first law

Newton's second law

Newton's third law

Explanation:

While all three laws come into play in a car crash only one is specifically responsible for keeping a person restrained in their seat. Just before the crash, the passenger is moving along at the same speed as the car. When the car collides into the other car and decelerates, the person's body continues to move forward. This is Newton's first law, or the law of inertia. But it is Newton's third law that keeps the person from being ejected from their seat. The force of the person's body moving forward was matched by that of the seatbelt. For every action there is an equal and opposite reaction. If the seat belt was unable to "match" the force of the person's body moving forward against it, it would have snapped and the person would have continued forward.

### Example Question #9 : Newton's Third Law

A locomotive is pushing a train at a constant velocity of . How does the force exerted by the locomotive on the train relate to the force of the train on the locomotive?

They are in opposite directions and have different magnitudes

They are the same in magnitude and opposite in direction

They are in the same direction and have the same magnitude

They are the same in both magnitude and direction

None of these

They are the same in magnitude and opposite in direction

Explanation:

This is Newtons's third law. Every action has an equal an opposite reaction. The reason the train is able to move at all is due to the force the locomotive puts on the rails, which enables it to accelerate the cars.

### Example Question #81 : Fundamentals Of Force And Newton's Laws

Two objects apply forces to each other. The force on one of the blocks as a function of time in the x-direction is , where  and  are constants. What's the force as a function of time in the x-direction on the other block? Assume no other forces are present besides the forces the objects apply to each other.