Conservation of Energy II Studio Physics I Review of Energy of a Cart on an Inclined Plane (with very low friction) Consider a cart given a quick push up an incline. The cart rolls up the ramp slowing down as it goes, reaches its highest point, and then rolls back down the ramp speeding up on the way. If there is very little friction, the graphs of the cart's gravitational potential energy Ug, kinetic energy KE and Mechanical Energy (Ug+KE) look like the graphs shown in file conserv4.mbl which on the web page or CD. Open this file now. Remember that you can only transfer the .mbl files with Internet Explorer. They do not transfer with Netscape. 1. Carefully explain in one complete sentence what "conserved" means in relation to conservation of energy. Is energy conserved if the initial and final values of the energy are the same but the amount of energy at intermediate moments of time are different? Is the kinetic energy of the cart conserved? Why or Why not? Is the gravitational potential energy of the cart conserved? Why or Why not? Is the mechanical energy conserved? Why or Why not? Check your answer with your TA or Professor either now or before you leave class. 2. Where does the cart get its initial energy? Where does the cart's energy go at the end of the motion, when the graph of mechanical energy in the conserv4.mbl file can be seen to have dropped down to zero? 3. We will now consider some specific points on the graphs of the cart's Ug, KE, and Mechanical Energy. Turn the analysis tool on by clicking on the 8th icon from the right (labeled x=?). Starting at time 0.9 second, measure and record neatly (as a table like the one shown below) the following values from the graphs: Ug, KE and Mechanical Energy. By how many Joules does the mechanical energy of the cart change over the entire time period from 0.9 seconds to 1.6 seconds? Time Ug KE Mechanical Energy 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 4. How is mechanical energy related to Ug and KE? 5. Calculate the change in the Ug and the change in KE between each time measured above. Calculate the change in the mechanical energy both by taking the sum of Ug and KE, and by taking the difference in the values recorded in your table from step #3. That is, make and fill in a table which looks like the one shown below. Recall that the change in a quantity is defined to be the final value minus the initial value. Time Ug KE Mechanical Energy Mechanical (from table in step#3) Energy (Ug+KE) 0.9 to 1.0 1.0 to 1.1 1.1 to 1.2 1.2 to 1.3 1.3 to 1.4 1.4 to 1.5 1.5 to 1.6 ©1999,2000 Cummings, Thornton, and Sokoloff 6. What is the average value of the change in mechanical energy? If you got a value of zero for the change in the mechanical energy does this mean that the value of the change in gravitational potential energy is zero too? If so, why? If not, what does a zero value for the change in mechanical energy indicate? Consider a cart given a quick push up an incline. Now there is a significant amount of friction between the cart and the track. The cart rolls up the ramp slowing down as it goes, reaches its highest point and then rolls back down the ramp speeding up on the way. 7. Make prediction graphs for the cart's gravitational potential energy Ug, kinetic energy KE and mechanical energy as a function of time. In making these predictions, it might be helpful to think about how these graphs will be the same as and different from the graphs for the same motion without friction that we have be analyzing. 8. Open the file conserv5.mbl (on the web page and CD). Compare the actual graphs shown to your predications and sketch the correct graphs on your paper. List at least 3 things that are different about these graphs as compared to those for the motion with very little friction. 9. Consider some specific points on the graphs of the cart's Mechanical Energy. Turn the analysis tool on by clicking on the 8th icon from the right (labled x=?). Starting at time 0.9 second, measure and record neatly (as a table like the one shown below) the Mechanical Energy. By how many Joules does the mechanical energy of the cart change over the entire time period from 0.9 seconds to 1.6 seconds? Time 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Mechanical Energy Mechanical Energy from previous time XXXXXX 10. Does the change in the mechanical energy average out to about zero? If not, where did the missing energy go? How much energy is lost during this time interval? 11. For the motion you are analyzing, the cart moves 17.7 cm during the time period from 0.9 seconds to 1.6 seconds. What is the force of friction between the cart and the track? ©1999,2000 Cummings, Thornton and Sokoloff