# AP Physics 1 : Newton's Second Law

## Example Questions

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### Example Question #61 : Fundamentals Of Force And Newton's Laws

force is applied to a block causing it to accelerate at  across concrete. The friction acts with  of force. What is the mass of the block?

Explanation:

We begin by drawing a free body diagram of the block.

is the force applied to the block.

is the weight of the block, or the force due to gravity. Weight is defined as  where  is the mass of the block and  is the gravitational constant.

is the normal force acting perpendicular to the contact surface.

is the force due to kinetic friction.

Newton's second law is  where  is the net force,  is the mass of the block and  is the acceleration.

We now apply Newton's second law in the direction of acceleration. In this problem, that is the x-direction.

Solving for mass, we have

There are two forces in the direction of acceleration,the applied force  and the force due to friction . Assuming that  is applied in the direction of acceleration and  is in the opposite direction,

. The problem tells us . Substituting in this information gives us

### Example Question #62 : Fundamentals Of Force And Newton's Laws

force is applied to a block causing it to accelerate at  across wood. The friction acts with  of force. What is the mass of the block?

Explanation:

We begin by drawing a free body diagram of the block.

is the force applied to the block.

is the weight of the block, or the force due to gravity. Weight is defined as  where  is the mass of the block and  is the gravitational constant.

is the normal force acting perpendicular to the contact surface.

is the force due to kinetic friction.

Newton's second law is  where  is the net force,  is the mass of the block and  is the acceleration.

We now apply Newton's second law in the direction of acceleration. In this problem, that is the x-direction.

Solving for mass, we have

There are two forces in the direction of acceleration,the applied force  and the force due to friction . Assuming that  is applied in the direction of acceleration and  is in the opposite direction,

. The problem tells us . Substituting in this information gives us

### Example Question #71 : Fundamentals Of Force And Newton's Laws

block accelerates at  across concrete. The coefficient of friction of concrete is . How much force was applied to the block?

Explanation:

We begin by drawing a free body diagram of the block.

is the force applied to the block.

is the weight of the block, or the force due to gravity. Weight is defined as  where  is the mass of the block and  is the gravitational constant.

is the normal force acting perpendicular to the contact surface.

is the force due to kinetic friction. Friction is defined as  where  is the coefficient of friction.

To find the force due to friction, we need to find  by applying Newton's second in the y-direction.

Newton's second law is  where  is the net force,  is the mass of the block and  is the acceleration.

There are two forces in the y-direction,  and . There are in opposite directions, so they are subtracted. We are given . There is no acceleration in the y-direction, so .

Substituting all this information into Newton's second law gives us

Assuming

Now that we have , we can find the force due to friction. Given that  and

We now apply Newton's second law in the direction of acceleration.  In this problem, that is the x-direction.

There are two forces in the direction of acceleration,the applied force  and the force due to friction . Assuming that  is applied in the direction of acceleration and  is in the opposite direction,

. The problem tells us  and . Substituting this information into Newton's second law gives us

### Example Question #72 : Fundamentals Of Force And Newton's Laws

block accelerates at  across wood. The coefficient of friction wood is . How much force was applied to the block?

Explanation:

We begin by drawing a free body diagram of the block.

is the force applied to the block.

is the weight of the block, or the force due to gravity. Weight is defined as  where  is the mass of the block and  is the gravitational constant.

is the normal force acting perpendicular to the contact surface.

is the force due to kinetic friction. Friction is defined as  where  is the coefficient of friction.

To find the force due to friction, we need to find  by applying Newton's second in the y-direction.

Newton's second law is  where  is the net force,  is the mass of the block and  is the acceleration.

There are two forces in the y-direction,  and . There are in opposite directions, so they are subtracted. We are given . There is no acceleration in the y-direction, so .

Substituting all this information into Newton's second law gives us

Assuming

Now that we have , we can find the force due to friction.  Given that  and ,

We now apply Newton's second law in the direction of acceleration. In this problem, that is the x-direction.

There are two forces in the direction of acceleration, the applied force  and the force due to friction . Assuming that  is applied in the direction of acceleration and  is in the opposite direction,

.  The problem tells us  and . Substituting this information into Newton's second law gives us

### Example Question #73 : Fundamentals Of Force And Newton's Laws

Suppose that a  box sits on top of a  box. A force is applied to the bottom box, causing both boxes to accelerate in the direction of the force. If the applied force remains the same, but the top box is removed, how does the acceleration of the system change?

The acceleration increases by a factor of

The acceleration decreases by a factor of

The acceleration decreases by a factor of

The acceleration increases by a factor of

The acceleration does not change

The acceleration increases by a factor of

Explanation:

To solve this question, we need to determine how the acceleration of the system changes once the top box is removed. To do this, we'll first have to evaluate the acceleration of the system before the top box is removed, and then do the same after its removal.

First, let's determine the initial acceleration. Since the applied force is causing both boxes to accelerate, we know that the total mass of the system has to be the combination of the masses of both boxes.

Next, we can write an expression for the final acceleration of the system, which will only consist of the bottom box.

Since the force applied doesn't change in either instance, we can relate each of the two expressions shown above.

Next, we can rearrange the above expression to isolate the term for final acceleration.

Now, we just need to plug in the values that we know to obtain our answer.

### Example Question #71 : Fundamentals Of Force And Newton's Laws

Force 1 pushes on a  ball with  to the right. Force 2 pushes on the ball with  to the left. Force 3 pushes on the ball with  to the left. The up and down forces can be assumed to be equivalent.

What is the acceleration of the ball?

to the left.

to the right.

to the right.

to the left.

to the right.

to the right.

Explanation:

Acceleration can be found by dividing the sum of the forces acting on an object by the mass of the object:

It is important to notice that both acceleration and the forces in the equation are vectors, meaning that both magnitude and direction matter.

In physics, we usually assign up and right as the positive directions, and down and left as the negative directions.

With that in mind, we first sum the forces:

Because our result is positive, the sum of the forces is directed towards the right.

Plugging in our sum and given mass in to our acceleration equation we find:

### Example Question #75 : Fundamentals Of Force And Newton's Laws

An person is riding upward in an elevator. The elevator is coming to a stop, accelerating at . What is the perceived weight of the person?

Explanation:

The person's perceived weight is a result of gravity and the elevator's acceleration changing the normal force between person and elevator. Using Newton's second law, we can express all of the forces in the y-direction as:

. Plugging in known values gives that

### Example Question #76 : Fundamentals Of Force And Newton's Laws

remote controlled helicopter is dropped from a height of . The spinning rotors in the helicopter create a constant upward force of . How long is the helicopter airborne before hitting the ground?

Explanation:

The only forces acting on the helicopter are the upward mechanical force and gravity. Newton's second law gives that the net force can be given by . The total acceleration can then be expressed as .

Using kinematics, we can find the time the helicopter is airborne. Using this kinematic equation , we can plug in known values and solve for time:

and

### Example Question #77 : Fundamentals Of Force And Newton's Laws

person slides down a  ladder to the ground. If they started from rest, slid down at constant acceleration, and touched the ground  later, what was the upward force on the person exerted by the ladder?

Explanation:

The only forces acting on the person are gravity and an unidentified opposing force that slows the person's descent.

Using kinematics, we can find the net acceleration of the person:

. Plugging in our known values, we find  and .

Using Newton's second law, we know that

. All of the forces in the y-direction can then be expressed as . Solving for  we find that

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