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/s2 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 𝑀 connected to the end of a string of length 𝐿 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 𝑀 has a value of 8.10 kg and 𝐿 has a value of 1.05 m, what is the angle 𝜃 of the pendulum when it is at its greatest height? Use a value of 9.81 m/s2 for the acceleration due to gravity. Give your answer to 3 significant figures.

Q8:

The figure shows a pendulum consisting of a mass 𝑀, on the end of a string of length 𝐿, hanging from a ceiling. The mass is at the greatest height of its path. If 𝑀 has a value of 5.50 kg, 𝐿 has a value of 1.30 m, and 𝜃 has a value of 12.0, 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/s2 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/s2 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 𝑀 at the end of a string of length 𝐿 hanging from a ceiling. Length is the vertical displacement of the mass above its equilibrium position when the pendulum is at an angle 𝜃. Which of the following gives the value of given 𝐿, 𝜃, and 𝑀?

  • A=𝐿(1+(𝜃))cos
  • B=𝐿(𝜃)sin
  • C=𝐿(1(𝜃))cos
  • D=𝐿(𝜃)cos
  • E=𝐿(1(𝜃))sin

Q17:

The figure shows a pendulum consisting of a mass 𝑀 on the end of a string of length 𝐿 hanging from a ceiling. The mass is at its greatest height in its motion. If 𝑀 has a value of 12 kg, 𝐿 has a value of 0.55 m, and 𝜃 has a value of 21, what will the speed of the pendulum as it passes through its equilibrium position be? Use a value of 9.81 m/s2 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

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.