# AP Physics 1 : Newton's Second Law

## Example Questions

### Example Question #11 : Newton's Second Law

In which of the following situations can we claim the net force is zero on the object described?

A child swinging on a swing set.

A bird taking flight from the ground.

Airplane changing direction to avoid a storm while maintaining a constant speed.

Elevator ascending at a constant speed.

Car breaking to a stop.

Elevator ascending at a constant speed.

Explanation:

Acceleration requires a change in one of two quantities: speed and direction

The elevator is traveling only upwards and at a non changing speed. The accleration is zero and thus the net force must be zero by newton's second law.

The bird taking flight is accelerating from rest to some non-zero speed. Net force is non zero because the speed changes.

The child on the swing set changes direction due to traveling in a semi-circle. Also their speed will change as well. Net force is non zero because both the speed and direction change.

The car breaking to a stop is changing speed. Net force is non zero because the speed changes.

The airplane, while maintaining a constant speed, changes direction and therefore accelerates. Net force is non zero because the direction changes.

### Example Question #11 : Newton's Second Law

A proton has a mass that's about  times the mass of an electron. Given that electrostatic forces between a proton and electron cause them to attract one another with the same force, what can you say about the acceleration of the two particles?

The acceleration of the electron is  of the acceleration of the proton.

The acceleration of the proton is the same as the acceleration of the electron.

The acceleration of the proton is  of the acceleration of the electron

The acceleration of the proton is  times the acceleration of the electron.

The acceleration of the proton is  of the acceleration of the electron

Explanation:

For this, we have to know that:

, where  is a force,  is an object's mass, and  is its acceleration.

The text tells us that the electrostatic force between the proton and electron will exert the same force, but that the mass of the proton is  times the mass of the electron.

, where  is the force on the proton and  is the force on the electron.

To determine the effect on their acceleration:

, where  and  are the masses of the proton and electron respectively, and  and  are the acceleration of the proton and electron respectively.

Since we know that

Solving for the acceleration of the proton:

The acceleration of the proton is  of the acceleration of the electron.

### Example Question #12 : Newton's Second Law

If a  object is subjected to a force of , by how much will it accelerate?

Explanation:

In this question, we're being told that an object of a given mass is being subjected to a force. To solve this problem, we'll need to make use of Newton's second law, which states that an object of a given mass will accelerate at a rate that is proportional to the force that is applied. Or, written in equation form:

Plugging in the values given, we obtain:

### Example Question #13 : Newton's Second Law

2 objects(named object A and object B) of equal masses and initial kinetic energy collide onto one another. During the collision, object A loses  of its kinetic energy, which object B gains. Assume mass of both objects remain unchanged.

Given that object A's mass is  and its velocity changes by  over a period of  seconds, determine the average force applied on object A.

Explanation:

Force is given by:

, where  is mass and  is acceleration.

We're given mass, but we aren't given acceleration. Since the question asks for average force , we can determine average acceleration

, where  is the change in velocity and  is change in time.

In our problem,  and

### Example Question #14 : Newton's Second Law

A block with a mass of  is pushed across a frictionless surface with a force of  for a time of . What is the velocity of the block after the push?

Explanation:

Here we must use the following formula:

We can substitute our known values of mass and force and solve for acceleration

Since we know the acceleration and the time it acts upon the object, we can determine the final velocity through the following equation:

### Example Question #15 : Newton's Second Law

Consider a block sitting at rest on an inclined plane. Find the maximum inclination angle the plane may have without the block sliding if the coefficients of kinetic and static friction are , respectively.

Explanation:

If the block is to remain at rest on the plane, we know that the sum of the forces acting a long the plane must be equal and opposite. This means that the gravitational force acting along the plane is equal to and opposite of the force of friction. This can be demonstrated as:

This can be rewritten as:

For the block to remain at rest, the force of static friction must exceed (for this problem we will set them equal to each other since it gives us the best approximation); solve for the angle:

### Example Question #16 : Newton's Second Law

A force of  is applied to a  object in space.

What is the acceleration of the object?

Explanation:

Newton's second law states:

Where  is the net force exerted upon an object,  is the mass of the object and  is the acceleration of the object.

We rearrange this equation to show:

Plug in our given values with  and :

### Example Question #11 : Newton's Second Law

If  of force is continuously applied to a box with mass , what will the box's velocity be after  given that it's initial velocity was

Explanation:

By Newton's second law:

, where  is force,  is mass, and  is acceleration.

This is the acceleration. Since we're assuming this acceleration is constant over time, we can model velocity  as:

where  is the initial velocity.

Since the initial velocity is  in our problem,

After  seconds,

### Example Question #18 : Newton's Second Law

A train of mass  goes from  to  in . Calculate the deceleration in terms of .

Explanation:

Use work:

All energy will be kinetic.

Convert  to :

Plug in values. Force will be negative as it is pointing against the direction of travel:

Solve for :

Use Newton's second law:

Plug in values:

Solve for :

Convert to

### Example Question #19 : Newton's Second Law

A train of mass  goes from  to  in . Estimate the coefficient of friction of the steel wheels on the steel rails. Assume the wheels are locked up.

Explanation:

Use work:

All energy will be kinetic.

Convert  to :

Plug in values. Force will be negative as it is pointing against the direction of travel:

Solve for :

Use frictional force:

Plug in values:

Solve for