# 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 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/s2 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/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 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/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