High School Physics : High School Physics

Study concepts, example questions & explanations for High School Physics

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Example Questions

Example Question #1 : Understanding Springs

A spring has a mass attached to one, which oscillates with a period of . What is the frequency?

Possible Answers:

Correct answer:

Explanation:

The mass has no bearing on the relationship between frequency and period. This relationship is given by the equation:

Given the period, the frequency will be equal to its reciprocal.

Example Question #1 : Harmonic Motion

A spring with a spring constant of is compressed . How much potential energy has been generated?

Possible Answers:

Correct answer:

Explanation:

The formula for the potential energy in a spring is:

Use the given spring constant and displacement to solve for the stored energy.

Example Question #1 : Harmonic Motion

A mass is placed at the end of a spring. It has a starting velocity of  and is allowed to oscillate freely. If the mass has a starting velocity of , what would the period be?

Possible Answers:

The period would be  as long.

The period would be half as long.

The period would be  times as long.

The period would remain the same.

The period would be twice as long.

Correct answer:

The period would remain the same.

Explanation:

When it comes to the period of a spring, the velocity of the object has no effect.

The equation is .

Example Question #2 : Harmonic Motion

A spring is attached to a mass, oscillating freely in simple harmonic motion. What change can be made to increase the period of the oscillation?

Possible Answers:

Increase the mass at the end of the spring

Use a spring with a greater spring constant

Decrease the mass at the end of the spring

Take the spring to a planet with a lower acceleration due to gravity

Lengthen the spring

Correct answer:

Increase the mass at the end of the spring

Explanation:

The equation for the period of a spring in simple harmonic motion is:

In this formula,  is the mass and  is the spring constant. The only two things we can adjust that can change the period, then, are the mass and spring constant. The length of the spring and the acceleration due to gravity are irrelevant.

If we increase the mass we get a larger numerator, which in turns will give us a larger period. If we decrease the mass we get a smaller numerator, which would give us a smaller period. If we use a higher spring constant we get a larger denominator, which also gives us a smaller period.

Example Question #3 : Harmonic Motion

What does the negative sign indicate in the equation below?

Possible Answers:

The spring constant, , is always negative 

The force, , acts in a negative direction

The force, , acts downwards 

The force, , acts in the opposite direction of the displacement, 

Correct answer:

The force, , acts in the opposite direction of the displacement, 

Explanation:

The correct answer is that the force acts in the opposite direction of the displacement.

The equation given is Hooke's law, which is used to determine spring force based on the spring constant, , and the displacement of the spring, .Negative and downward are arbitrary, and spring constants are always positive. If a spring is stretched or compressed in a given direction, the force of the spring will always act opposite the direction of the displacement in order to return the spring to the resting equilibrium position.

Example Question #1 : Understanding Pendulums

A pendulum is dropped from rest at  above the ground. If no outside forces (except gravity) are acting upon it, what will be its maximum height on the other side?

Possible Answers:

Less than 

Greater than 

Correct answer:

Explanation:

If no outside forces act upon the pendulum, it will continue to oscillate back to the original height of 

The proof of this is in the law of conservation of energy. At the top, the pendulum has all potential energy, which is given by the formula . As it swings, the potential energy is converted to kinetic energy until, at the bottommost point, there is only kinetic energy. It then changes direction and begins to rise again. When it rises to the maximum height on the other side, all of its kinetic energy will turn back into potential energy.

Mathematically, the initial and final potential energies are equal.

Notice the masses and gravity can cancel out on both sides, as neither of these will change. This leaves us with only height.

Example Question #1 : Harmonic Motion

A mass on a string is released and swings freely. Which of the following best explains the energy of the pendulum when the string is perpendicular to the ground?

Possible Answers:

The mass has maximum kinetic energy

The mass has equal amounts of kinetic and potential energy

The mass has mostly kinetic energy, but there is some potential energy

The mass has maximum potential energy

The mass has mostly potential energy, but there is some kinetic energy

Correct answer:

The mass has maximum kinetic energy

Explanation:

Conservation of energy dictates that the total mechanical energy will remain constant. Initially, the mass will not be moving and will be at its highest height. When released, it will begin to travel downward (lose potential energy) and gain velocity (gain kinetic energy). When the mass reaches the bottommost point in the swing, the potential energy will be at a minimum and the kinetic energy will be at a maximum. This point corresponds to the string being perpendicular to the ground.

Example Question #1 : Harmonic Motion

A man swings a bucket back and forth at the end of a rope, creating a pendulum. What factor could be used to increase the period of the pendulum?

Possible Answers:

Add water to the bucket

Increase the length of the rope

Remove water from the bucket

Move the pendulum to a lower altitude

Use a stronger rope

Correct answer:

Increase the length of the rope

Explanation:

The equation for the period of a pendulum is:

Notice that the material of the pendulum and the mass at the end do not enter into the equation at all. The only things that are capable of affecting the period are are the length of the pendulum and the acceleration due to gravity.

While changing the altitude of the pendulum will change the period, it will do it only slightly unless you take it miles above the earth's crust. Furthermore, decreasing the altitude of the pendulum will increase the force due to gravity, which will resulut in a decreased period. The best answer is to increase the length of the rope. This will increase the period of the pendulum.

Example Question #1 : Using Spring Equations

A spring with a spring constant of  is compressed . What is the potential energy stored in the spring?

Possible Answers:

Correct answer:

Explanation:

The equation for spring potential energy is .

Plug in the given values for the distance and spring constant to solve for the potential energy.

Remember, since the spring was compressed, it has a negative displacement. The resultant potential energy will be positive as, when released, the displacement will be along the positive horizontal axis.

Example Question #2 : Harmonic Motion

A spring has a spring constant of .

What force is required to compress it ?

Possible Answers:

Correct answer:

Explanation:

For this problem, use Hooke's law:

In this formula,  is the spring constant,  is the compression of the spring, and  is the necessary force. We are given the values for the spring constant and the distance of compression. Using these terms, we can sovle for the force of the spring.

Plug in our given values and solve.

Note that the force is negative because it is compressing the spring, pushing against the coil. When the force is released, the equal and opposite force of the spring will cause it to extend in the positive direction.

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