# AP Physics 1 : Newton's Second Law

## Example Questions

### Example Question #41 : Newton's Second Law

A truck is pulling a trailer and is accelerating at . The truck has mass and the trailer has mass . Determine the force the truck is applying on the trailer. Ignore friction.

None of these

Explanation:

The mass of the truck is irrelevant to this problem.

The trailer has a mass of , and is accelerating at , thus, using

### Example Question #42 : Newton's Second Law

A truck is pulling a trailer and is accelerating at . The truck has mass  and the trailer has mass . Determine the force and direction the trailer is applying on the truck.

, backwards

, backwards

, backwards

, forwards

, forwards

, backwards

Explanation:

The mass of the truck is irrelevant to this problem.

The trailer has a mass of , and is accelerating at .

This is the force the truck is applying to the trailer to accelerate it forward. Based on Newton's Laws, the trailer is applying the same force, in the opposite direction.

### Example Question #43 : Newton's Second Law

force is applied to a block causing it to accelerate at  across a sheet of ice. 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.

Since the block is on ice, there is no friction.

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

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

Solving for mass, we have

The only force in the direction of acceleration is the applied force , therefore

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

### Example Question #44 : Newton's Second Law

force is applied to a  block sitting on a sheet of ice. What is the acceleration 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.

Since the block is on ice, there is no friction.

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

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

Solving for acceleration, we have

The only force in the direction of acceleration is the applied force , therefore

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

### Example Question #41 : Newton's Second Law

force is applied to a  block sitting on a sheet of ice. What is the acceleration 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.

Since the block is on ice, there is no friction.

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

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

Solving for acceleration, we have

The only force in the direction of acceleration is the applied force , therefore

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

### Example Question #46 : Newton's Second Law

force is applied to a block causing it to accelerate at  across a sheet of ice. 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.

Since the block is on ice, there is no friction.

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

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

Solving for mass, we have

The only force in the direction of acceleration is the applied force , therefore

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

### Example Question #47 : Newton's Second Law

block accelerates at  across a sheet of ice. 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.

Since the block is on ice, there is no friction.

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

Newton's second law is .

Where  is the net force applied in the direction of acceleration,  is the mass of the block and  is the acceleration.

The only force in the direction of acceleration is the applied force , therefore .  The problem tells us  and . Substituting in this information gives us:

### Example Question #48 : Newton's Second Law

block accelerates at  across a sheet of ice. 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.

Since the block is on ice, there is no friction.

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

Newton's second law is .

Where  is the net force applied in the direction of acceleration,  is the mass of the block and  is the acceleration.

The only force in the direction of acceleration is the applied force , therefore . The problem tells us  and . Substituting in this information gives us

### Example Question #49 : Newton's Second Law

force is applied to a  block sitting on concrete. The coefficient of friction of concrete is . What is the acceleration 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.  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.

Solving for acceleration, 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 #50 : Newton's Second Law

force is applied to a  block sitting on wood. The coefficient of friction of wood is . What is the acceleration 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.  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.

Solving for acceleration, 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