# Worksheet: The Mechanical Energy of a Pendulum

In this worksheet, we will practice calculating the gravitational potential energy and kinetic energy of a pendulum at different points in its motion.

**Q1: **

In one complete oscillation of a pendulum, how many times does the pendulum have its peak kinetic energy?

**Q2: **

Each of the following diagrams shows a pendulum at different points in its motion. Which diagram shows the point where the pendulum has the most kinetic energy?

- A
- B
- C
- D
- E

**Q3: **

A pendulum with a mass of 5.00 kg
and a length of 0.800 m has a kinetic energy of 2.60 J when it passes through its equilibrium position. What is the maximum angle to the vertical that the pendulum reaches? Use a value of 9.81 m/s^{2} for the acceleration due to gravity. Give your answer to 3 significant figures.

**Q4: **

Which of the lines on the graph correctly shows how the mechanical energy of a pendulum varies with time?

- AThe orange line
- BThe red line
- CThe violet line
- DThe blue line
- EThe black line

**Q5: **

The graph shows the kinetic energy of a pendulum over time. What is the period of the pendulum?

**Q6: **

Which of the lines on the graph correctly shows how the kinetic energy of a pendulum varies with time?

- AThe orange line
- BThe violet line
- CThe red line
- DThe black line
- EThe blue line

**Q7: **

The figure shows a pendulum consisting of a mass connected to the end of a string of length that is hanging from a ceiling. When the mass is at the greatest height of its path, it has a gravitational potential energy of 2.30 J. If has a value of 8.10 kg and has a value of 1.05 m, what is the angle of the pendulum when it is at its greatest height? Use a value of 9.81 m/s^{2} for the acceleration due to gravity. Give your answer to 3 significant figures.

**Q8: **

The figure shows a pendulum consisting of a mass , on the end of a string of length , hanging from a ceiling. The mass is at the greatest height of its path. If has a value of 5.50 kg, has a value of 1.30 m, and has a value of , what is the difference in the gravitational potential energy of the mass between its position at its greatest height and its equilibrium position? Use a value of 9.81 m/s^{2} for the acceleration due to gravity. Give your answer to 3 significant figures.

**Q9: **

A pendulum with a mass of 4.00 kg and a length of 2.50 m
has a speed of 1.20 m/s
when it passes through its equilibrium position. What is the maximum angle to the vertical
that the pendulum reaches? Use a value of 9.81 m/s^{2} for the acceleration due to gravity. Give your answer to 3 significant figures.

**Q10: **

Each of the following diagrams shows a pendulum at different points in its motion. Which diagram shows the point where the pendulum has the least gravitational potential energy?

- A
- B
- C
- D
- E

**Q11: **

The graph shows the kinetic energy of a pendulum over time. What is the frequency of the pendulum?

**Q12: **

The graph shows the gravitational potential energy of a pendulum over time. What is the period of the pendulum?

**Q13: **

The graph shows the gravitational potential energy of a pendulum over time (the red line) and the kinetic energy of the pendulum over time (the blue line). What does the black line represent?

- AThe rotational kinetic energy
- BThe work done
- CThe velocity
- DThe mechanical energy
- EThe momentum

**Q14: **

In one complete oscillation of a pendulum, how many times does the pendulum have its peak gravitational potential energy?

**Q15: **

The graph shows the gravitational potential energy of a pendulum over time. What is the frequency of the pendulum?

**Q16: **

The figure shows a pendulum consisting of a mass at the end of a string of length hanging from a ceiling. Length is the vertical displacement of the mass above its equilibrium position when the pendulum is at an angle . Which of the following gives the value of given , , and ?

- A
- B
- C
- D
- E

**Q17: **

The figure shows a pendulum consisting of a mass on the end of a string of length hanging from a ceiling. The mass is at its greatest height in its motion. If has a value of 12 kg, has a value of 0.55 m, and has a value of , what will the speed of the pendulum as it passes through its equilibrium position be? Use a value of 9.81 m/s^{2} for the acceleration due to gravity. Give your answer to 3 significant figures.

**Q18: **

Which of the lines on the graph correctly shows how the gravitational potential energy of a pendulum compared to that at its equilibrium position varies with time?

- AThe orange line
- BThe blue line
- CThe black line
- DThe violet line
- EThe red line