Lesson 1 - Atwood's Pulley (massless pulley)

In order to assign a numerical value to the potential energy of a body, it is first necessary to define a "zero point" or reference level at which the potential energy is considered to be 0 J. You do this on the applet by repositioning the Ep Reference line by moving it up or down. To see how this works, position the Ep Reference line to be at the same height as the centre of the pulley as shown in the next diagram.

Set mass 1 to equal 250 g and mass 2 to be 750 g.

1. Are the initial potential energies for mass 1 and mass 2 positive, negative, or zero in this case? Explain your answer.

2. Run the applet (click ), and produce a graph showing the potential energy for each mass as a function of time. Explain why the graphs look the way they do.

3. Mass 1 climbs by 1.133 m and mass 2 drops by 1.133 m. Calculate the change in potential energy for each mass. Recall that , where ΔE_p is the change in potential energy, m is the mass, g = acceleration of gravity and Δh is the change in height. Show how the change in energy for each mass can be measured from the graphs that you produced in question 2.
   
   
   
   
   
   
   
4. Its clear that we didn't pick the most convenient place for the Ep Reference line. "Reset" the applet ( ) and this time put the Ep Reference line through the yellow dot that represents the centre of mass for mass 1. When released, mass 1 will move above this line and its Ep will increase. Since mass 2 is already above this line and it drops, its Ep will start at its maximum value and then decrease. Calculate the initial potential energy for mass 2 relative to this new Ep Reference line and use the applet to verify your calculation (hint: redo the graphs that you created in question 2). What is the initial potential energy for mass 2?
   
   
   
   
   
   
5. Combine the initial potential energy for each mass (Ep1 + Ep2). This represents the initial potential energy for the system. What is this energy? Run the applet. What is the potential energy of the system now? Are these two energies the same?
   
   
   
   

In the previous example the initial potential energy of the system was greater than the final potential energy (by about 5.56 J). What happened to this energy?

Answer: When you click "Play", the masses begin to accelerate. Mass 1 moves up, mass 2 moves down. A new energy form, kinetic energy, is now being created. Recall, kinetic energy is given by the expression , where m is the mass and v is the velocity.

1. Rerun the applet using the same mass values used in the previous section. Produce kinetic energy-time graphs for each mass and a graph showing velocity-time (the velocity will be the velocity for mass 2 - mass 1's velocity is just the negative of this). Your graph should look something like the one shown next.

2. How fast is each mass moving at t = 0.50 s? What is the kinetic energy for each mass at this time? Answer this by calculating the kinetic energy and then verify this result by inspecting the graph. (Tip: use the "drag-and-zoom" control button to zoom-in on points of interest on the graph. Alternately, generate a data table and look up the velocity and energy at t = 0.50 s.)
   
   
   
   
   
   
   
   

3. The total energy of the system is just the sum of all the kinetic and potential energy terms at any instant. Find the total energy of this system at t = 0.00 s, t = 0.50 s and t = 0.68 s. What do you notice about these three numbesr?