# AP Physics C Electricity : Mechanics Exam

## Example Questions

### Example Question #10 : Using Spring Equations

All angles in this problem are expressed in radians.

An object oscillates horizontally, and its displacement from equilibrium can be found using the equation:

where  is in seconds. What is the velocity of the object at ?

Explanation:

To find the equation for velocity, we take the first derivative of the position function. Don't forget the chain rule for the inside of the cosine!

### Example Question #11 : Harmonic Motion

A mass on the end of a spring oscillates back and forth. The period of an oscillating spring is measured to be 2.27 seconds. The mass is measured to be 0.300 kg. What is the spring's spring constant?

Explanation:

To solve this problem, we can use the following equation:

Here,  is the period of an oscillation,  is the mass of the oscillating thing in kg, and  is the spring constant in .

Rearranging the equation to solve for the spring constant, , we get:

Plugging in the two known values, we get:

Solving for , we get .

### Example Question #12 : Harmonic Motion

A  block on a frictionless table is connected to a horizontal spring with constant . If the block is released from rest when the spring is stretched a distance of ,

what is its speed when the spring is compressed a distance of ?

Explanation:

Assuming this is a frictionless table, we don't have to take the work done by friction into account.

This is a conservation of energy problem. In this problem we have to realize that the potential energy of the spring at  is equal to the kinetic energy of the spring at + the potential energy of the spring at .

This can be shown in the following equation:

If we solve for , we get the following equation:

Remember to convert the distances given in centimeters to meters.

If we plug in all the variables, we get

### Example Question #1 : Using Pendulum Equations

A simple pendulum of length  swings at a radius  from a fixed point on the ceiling. As it moves, the pendulum creates an angle  with the line that extends vertically downwards from the fixed point. At what angle does the mass attached to the pendulum have the highest kinetic energy?

Explanation:

The correct answer is . Since the pendulum is at the bottom of its motion at this point, it has the lowest amount of energy given to gravitational potential and thus, the highest kinetic energy.

### Example Question #2 : Using Pendulum Equations

If a simple pendulum is constructed using a  rope of negligible weight and a large steel ball weighing . What is the period of the pendulum?

Not enough information

Explanation:

Use the equation for the period of a simple pendulum:

Here,  is the period in seconds,  is the length of the pendulum in meters, and  is the acceleration due to gravity in .

We can plug in the given quantities for length and acceleration to solve for the period.

Note that the mass of the rope as negligible. We also need not incorporate the extraneous information regarding the weight of the steel ball attached to the pendulum. This does not influence the period of this simple pendulum.

### Example Question #13 : Harmonic Motion

A block of mass  is attached to two springs, each of whose spring constant is . The ends of the springs are fixed, and the block is free to move back and forth. It is released from rest at an initial amplitude, and its period is measured to be . What would the period be if the spring on the right side were to be moved to the other side, attached along side of the other spring?

Explanation:

Because the springs are effectively in a parallel arrangement already, moving one does not change the effective spring constant, and therefore does not affect the period.

### Example Question #1 : Circular Motion

A ball of mass  is tied to a rope and moves along a horizontal circular path of radius  as shown in the diagram (view from above). The maximum tension the rope can stand before breaking is given by . Which of the following represents the ball's linear velocity given that the rope does not break?

None of these

Explanation:

This is a centripetal force problem. In this case the tension on the rope is the centripetal force that keeps the ball moving on a circle.

If we want for the rope not to break, then the tension should never exceed .

Now we just solve for velocity:

### Example Question #1 : Rotational Motion And Torque

What is the rotational equivalent of mass?

Moment of inertia

Torque

Angular momentum

Moment of inertia

Explanation:

The correct answer is moment of inertia. For linear equations, mass is what resists force and causes lower linear accelerations. Similarly, in rotational equations, moment of inertia resists torque and causes lower angular accelerations.

### Example Question #2 : Rotational Motion And Torque

In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?

Torque

Angular acceleration

Moment of inertia

Impulse

Torque

Explanation:

Just as force causes linear acceleration, torque causes angular acceleration. This can be seen most in the linear-rotational comparison of Newton's second law:

### Example Question #3 : Rotational Motion And Torque

A boot is put in a  stick which is attached to a rotor. The rotor turns with an angular velocity of . What is the linear velocity of the boot?