Physics 151: Computerized Recitation #7

Conservation of Energy


This recitation will focus on applications of the conservation of energy. Please experiment with the Physlet simulations below and complete the required calculations on your worksheet.


Simulation 1: Gravitational Potential Energy - Pendulum


The physlet above allows you to watch a pendulum swinging back and forth. You may use the pause button to stop the animation and the step buttons to move through the animation frame by frame. You can click anywere on the grid and read out the x and y values (assume units are in meters) of the cursor location. Click Simulate! below to begin the animation.

Select Pendulum Length (m): Select Amplitude (°): Bob Mass (kg):

Output Total Energy (J): Output Velocity at Equilibrium Position (m/s):

Suggestions for Exploration



Simulation 2: Elastic Potential Energy - Spring


The animation above displays the motion of a mass oscillating on a horizontal spring. Pistons with arbitrary units display the amount of kinetic energy and elastic potential energy of the spring-mass system.

Select Spring Constant (N/m): Select Amplitude (m): Bob Mass (kg):

Output Total Energy (J): Output Maximum Velocity (at Equilibrium Position) (m/s):

Suggestions for Exploration

  • Setup the simulation for a spring constant of 40 N/m, an amplitude of 0.4 m, and a mass of 3.0 kg. The potential energy at its release point (maximum amplitude) is:

    • Since the kinetic energy at the release point is zero and the potential energy at the equilibrium position is zero, the conservation of energy can be stated simply as the potential energy at the release point must be equal to the kinetic energy at the equilibrium point. This relation can then be used to solve for the (maximum) velocity at the equilibrium point.

    We can also solve for the velocity at an arbitrary position such as x = 0.3m.

  • Experiment with several other values of spring constant, amplitude, and mass and try to predict the total energy and the maximum velocity. Use the simulation output boxes to check your answers.
  • Can you determine the values of the unknown variables? Feedback


Simulation 3: Elastic Potential Energy - Spring Gun


The simulation above depicts a spring loaded toy cannon siting on a platform 1.55 m above a tabletop. A cannon ball can be pushed into the cannon compressing the spring 0.15 m. The cannonball can then be fired horiztonally and we can predict how far it travels before reaching the level of the tabletop. This simulation effectively utilizes the principles of kinematics and energy conservation.

Select Spring Constant (N/m): Select Projectile Mass (kg):
Output Total Energy (J):  Output Horizontal Velocity (at Equilibrium Position) (m/s): Output Horizontal Distance (m):

Suggestions for Exploration

  • Setup the simulation for a spring constant of 1600 N/m and a mass of 2.0 kg. When the cannon is fired the elastic potential energy is converted in kinetic energy.

    • From this point on it is a horizontal launch problem. We can find the horizontal distance traveled by multiplying this velocity by the time in the air.

  • Experiment with several other values of spring constant and mass and try to predict the horizontal distance traveled by the cannonball. Use the simulation output boxes to check your answers.
  • Can you determine the values of the unknown variables? Feedback
  • Super Duper Bonus Question: Can you predict the velocity that the ball will have when it hits the ground. Feedback