# Conservation of Energy

Simulation Used: The Ramp from the PhET at the University of Colorado.
• Initial settings:
• Choose an object from the list on the right and write down its mass, and the coefficient of friction.
• Set the initial position of the object at 15.0 m (top of the ramp)

• Activity 1: Check whether the mechanical energy is conserved in the absence of friction.
• Click the box on the menu on the right, so that the ramp is frictionless. (If the object starts sliding, stop the simulation and re-do the initial settings.)
• Below the picture, click and make the energy graph visible.
• Minimize any other graphs.
• Perform the experiment:
• Set the ramp angle equal to 2o and start the simulation.
• Stop the object at one position and write down its position, kinetic, and potential energy at that position (the reading is on the energy diagram below the ramp)
• Resume sliding the object.
• Stop the object at a second position and again write down its position, kinetic and potential energy
• Repeat the procedure for ramp angles: 4o, 6o
• Record your measurements in the following table:

 Angle x1 (m) KE1 (J) PE1 (J) E1 (J) x2 (m) KE2 (J) PE2 (J) E2 (J) $\frac{\left|E_2-E_1\right|}{E_1}\times&space;100&space;\%$ 2o 4o 6o

NOTES:
• The total mechanical energy E = KE + PE. Use your calculators rather than using the value from the simulation.
• The last column in the table above is the relative difference (percent error) in the total mechanical energy.
• Results: Does the total mechanical energy of the object remain constant throughout the sliding? By what percentage do the two energies differ (the last column of your data table)?

• Activity 2: Verify the Work-Energy relation
• Choose another object and write down its mass and the coefficient of friction between the object and the ramp.
• Click and expand the Work diagram (below the energy diagram)
• Keep the energy diagram visible.
• Below the picture, click and make the energy graph visible. Minimize any other graphs.
• Unclick the "Frictionless" box. If the simulation starts, stop it and re-do the settings if necessary.
• Perform the experiment:
• Set the ramp angle equal to 10o and start the simulation.
• Stop the object at one position and write down its position (x1), kinetic energy (KE1), potential energy (PE1), and the work done by the friction up to that position (W1).
• Resume sliding the object.
• Stop the object at a second position and again write down its position (x2), kinetic energy (KE2), potential energy (PE2), and the work of the friction done on the object up to that position (W2).
• Repeat the procedure for the ramp angles of 12o, and 14o
• Record your data in the following table:

 Angle x1 KE1 PE1 E1 W1fr x2 KE2 PE2 E2 W2fr Degrees (m) (J) (J) (J) (J) (m) (J) (J) (J) (J) 10o 12o 14o

NOTES:
• Do not use the value for the total mechanical energy from the simulation, but rather calculate it yourself as the sum of the kinetic and potential energies: E = PE + KE.
• The work given by the simulation at any given point is the total amount work done by the friction starting from the initial position (15 m) up to the current position. Thus, if you need to know the work done by the friction from point 1 to point 2, you need to subtract the two values for the friction given by the simulation. That is: W12 = W2 - W1.

• Results:
• In the table below, write down your results for the total mechanical energy of the object at location 1 (E1  =  KE1&nbps;+ PE1), and at location 2 (E2  =  KE2&nbps;+ PE2), and the Work done by friction between the p.1 and p.2 (W12 = W2 - W1).
 Angle x1 E1 x2 E2 W12 Degrees (m) (J) (m) (J) (J) 10o 12o 14o

• Questions:

Is the mechanical energy at position 1 equal to that at position 2?

Where has the missing energy gone?

Is the change in the mechanical energy from position 1 to position 2 equal the amount of the frictional work done between the two positions?