Understanding Newton's Third Law

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1

Two skaters push off of each other in the middle of an ice rink. If one skater has a mass of and an acceleration of , what is the acceleration of the other skater if her mass is ?

Explanation

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the mass of each skater and the acceleration of the first. Using these values, we can solve for the acceleration of the second.

From here, we need to isolate the acceleration of the second skater.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector.

2

Two skaters push off of each other in the middle of an ice rink. If one skater has a mass of and an acceleration of , what is the mass of the other skater if her acceleration is ?

Explanation

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the acceleration of each skater and the mass of the first. Using these values, we can solve for the mass of the second.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector. From here, we need to isolate the mass of the second skater.

3

A boy falls out of a tree and hits the ground with of force. How much force does the ground exert on the boy?

We must know the mass of the boy to solve

Explanation

Newton's third law states that when one object exerts a force on another object, that second object exerts a force of equal magnitude, but opposite in direction on the first.

That means that:

Using the value from the question, we can find the force of the ground on the boy.

4

Two skaters push off of each other in the middle of an ice rink. If one skater has a mass of and an acceleration of , what is the mass of the other skater if her acceleration is ?

Explanation

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the acceleration of each skater and the mass of the first. Using these values, we can solve for the mass of the second.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector. From here, we need to isolate the mass of the second skater.

5

Basic Computational

A rock strikes a window with of force. How much force does that window exert on the rock?

We need to know the mass of the rock to solve

We need to know how long the two were in contact to solve

Explanation

Newton's third law states that when one body exerts a force on another body, the second body exerts a force equal in magnitude, but opposite in direction, on the first body.

Mathematically, this process can be written as:

Since the rock exerts of force on the window, then the window must exert of force on the rock.

6

A boy falls out of a tree and hits the ground with of force. How much force does the ground exert on the boy?

We must know the mass of the boy to solve

Explanation

Newton's third law states that when one object exerts a force on another object, that second object exerts a force of equal magnitude, but opposite in direction on the first.

That means that:

Using the value from the question, we can find the force of the ground on the boy.

7

Conceptual

If you exert a force F on an object, the force which the object exerts on you will

Depend on whether or not the object is moving

Depend on whether or not you are moving

Depend on the relative masses of you and the object

Always be F

Explanation

According to Newton’s 3rd Law of Motion, the force that is exert by object A onto object B is equal in magnitude and opposite in direction to the force that is exerted by object B onto object A. It is not dependent on the mass or motion of the object.

8

An object of mass m sits on a flat table. The Earth pulls on the object with force mg, which is the action force. What is the reaction force?

The table pushing up on the object with force

The object pushing down on the table with force

The table pushing down on the floor with

The object pulling upward on the earth with force

Explanation

There is a common misconception that the force that Earth pulls on the object is balanced by a reaction force of the table pushing up on the object. Though it is true that the magnitude between these forces are the same, they are not considered action reaction pairs.

According to Newton’s 3rd law the force with which object A acts on object B is equal and opposite to the force that object B acts on object A. In this case the initial force is the Earth pulling on the object. Therefore the pair would be the object pulling on the Earth.

If we consider the table we are adding a third object to the mix, which cannot be an action reaction pair. Therefore the normal force and the force of gravity are never considered action reaction pairs as they are two different forces acting on the same object.

9

Which of Newton's laws explains why it is easy for you to lift a 1L jug of milk from the fridge, but impossible to lift a 1000L jug?

More than one of these

Newton's first law

Newton's third law

Newton's second law

None of these

Explanation

The answer is more than one. The two laws that come into play are Newton's first and second laws. Newton's first law is best known as the law of inertia. It states that an object in motion will stay in motion and an object at rest will stay at rest unless acted on by an outside force. Newton's second law relates the acceleration of an object to the mass and the forces acting on it with the equation . An object won't move or stop moving unless the forces acting on it are imbalanced. In the case of the milk jug, it remained at rest until an outside force, your hand, acted upon it, demonstrating Newton's first law. The second law is applicable because the amount of acceleration of the two milk jugs is inversely related to their mass. It takes a much stronger force to move the 1000L milk jug than it does the 1L milk jug. The acceleration is also much smaller for the two objects when the same force is applied because one weighs so much more than the other. You can visualize this by rearranging the second law equation: . It is also beneficial to think in terms of two objects. Which is will accelerate more when you try and move it with the same force, a tennis ball or an elephant?

10

A ball is suspended from the ceiling by means of string. The Earth pulls downward on the ball with its weight force of . If this is the action force, what is the reaction force?

The string pulling upward on the ball with a force

The ceiling pulling upward on the string with a force

The string pulling downward on the ceiling with a force

The ball pulling upward on the earth with a force

Explanation

There is a common misconception that the force that Earth pulls on the object is balanced by a reaction force of the string pulling upward on the object. Though it is true that the magnitude between these forces are the same, they are not considered action reaction pairs.

According to Newton’s 3rd law the force with which object A acts on object B is equal and opposite to the force that object B acts on object A. In this case the initial force is the Earth pulling on the object. Therefore the pair would be the object pulling on the Earth.

If we consider the table we are adding a third object to the mix, which cannot be an action reaction pair. Therefore the tension force and the force of gravity are never considered action reaction pairs as they are two different forces acting on the same object.

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