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