Conservation of Energy

• Initial settings:
  • Choose the "Crate" and write down its mass.
  • Set the initial position of the crate at 15.0 m


• Activity 1: Check whether the mechanical energy is conserved in the absence of friction.
  • Additional Settings:
    • Click the box on the menu on the right, so that the ramp is frictionless. (If the crate 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 2^o and start the simulation.
    • Stop the crate at one position and write down in your notebook the position, the kinetic and the potential energy at that position (the reading is on the energy diagram below the ramp)
    • Continue the sliding.
    • Stop the crate at a second position and write down again the position, the kinetic and the potential energy
    • Repeat the procedure for ramp angles: 2^o, 4^o, 6^o, 8^o, and 10^o.
  • In your lab notebook, write down the data in the following format:
    
    

    DATA AND RESULTS

    Angle	x1 (m)	KE1 (J)	PE1 (J)	E1 (J)	x2 (m)	KE2 (J)	PE2 (J)	E2 (J)	% Error = |E2-E1|/((E2+E1)/2)
    2o
    4o
    6o
    8o
    10o

    
    NOTE!!! Do not write down directly the value for the total mechanical energy. Instead, add the values for the Kinetic and the Potential Energy using your calculators and write down that number in your data table.
    
  • Results: Does the total mechanical energy of the crate 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
  • Additional Settings:
    • Choose the "Sleepy Dog" and write down its mass and the coefficient of friction between the dog 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 10^o and start the simulation.
    • Stop the dog at one position and write down in your notebook the position, the kinetic, the potential energy, and the work done by the friction at that position.
    • Continue the sliding.
    • Stop the dog at a second position and write down again the position, the kinetic, the potential energy, the work of the friction.
    • Repeat the procedure for the ramp angles of 10^o, 12^o, and 14^o
  • NOTE!!! Do not write down directly the value for the total mechanical energy. Instead, add the values for the Kinetic and the Potential Energy using your calculators and write down that number in your data table.
    
  • In your lab notebooks, write down the data in the following format:
    
    

    DATA TABLE

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

    
    
  • Results: 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?
    
    The work done by the friction between positions x₁ and x₂ is the difference in the total work up to x₁, W₁, and the total work up to x₂, W₂. Thus,
    
         W_fr=W₁-W₂
    
    The balance of the total mechanical energy then becomes:
    
         E₁ + W_fr = E₂
    
    In order to verify the balance of energy, we calculate the percent difference between (E₁ + W_fr) and (E₂) as:
    
         | (E₁ + W_fr) - (E₂) | / (E₂)
    
    Record your calculations in the Results Table below:
    
    

    RESULTS TABLE

    Angle	x1	E1	Wfr	x2	E2	% Difference
    Degrees	(m)	(J)	(J)	(m)	(J)	| (E1 + Wfr) - (E2) |
    10o
    12o
    14o