Download Introduction to Conservation of Energy

Introduction to Conservation of Energy
Studio Physics I
In this activity, we consider a cart given a quick push up an inclined track.
Set up your equipment as follows:
The motion detector is at the very top of the track.
The end of the track should not hang off of the table.
A block of wood is placed under the end of the track at the very edge (right at the end).
The far end of the track is elevated about 2 inches by the block of wood.
The motion we will investigate is this:
The cart rolls up the ramp moving toward the motion detector, slowing down as it goes, reaches its highest point
and then rolls back down the ramp speeding up on the way. The cart is then caught at the bottom of the track.
Don’t let the cart get closer to the motion detector than 50 centimeters.
1. Sketch predictions of the velocity-time and position-time graphs for the cart (you can ignore friction). Show
the push and the catch of the cart. Take the positive direction to be away from the detector (down the incline).
2. Describe the direction of the force acting on the cart (it is zero, up the incline, down the incline?) and nature
of the force acting on the cart (it is constant, increasing, decreasing?) as:
a) The cart moves up the inclined plane, slowing down as it goes.
b) At the cart's highest point,
c) As the cart moves back down the inclined plane, speeding up as it goes.
3. Open the file “Conservation of Energy.MBL”. You can get the file under the “activities” icon on the web
page. The file is at the bottom of the activities list. Set up the equipment as discussed above and collect data for
the motion described in the box at the top of the page. Don’t let the cart get closer to the motion detector than
50 centimeters. Sketch the graphs of position vs time and velocity vs time on your activity sheet. Mark the turn
around (or highest) point on both of your graphs. Compare this graph to the prediction that you made in Step 1.
If the graphs are not VERY similar, either the prediction or the data is wrong. Determine which one it is. Collect
better data if necessary.
4. Sketch a prediction graph of the kinetic energy (the energy due to motion) of the cart over time as it moves.
Keep in mind that the kinetic energy (KE) is 1/2mv2 where m is the mass of the cart (in this case 0.5 kg) and v is
the velocity. When during the motion is the kinetic energy zero (at the top?, bottom?…)? When during the
motion is the KE a maximum? (Write your answers to these questions to the right of your sketch).
5. Change the velocity-time graph so that it displays the kinetic energy of the cart as a function of time. (This is
done by placing the cursor tip over the word "velocity " on the y-axis of the velocity-time graph and clicking the
left mouse button. Uncheck “velocity” and check “kinetic energy”.) Compare the actual graph of the cart's
kinetic energy to your prediction, and sketch the correct graph now. Mark on your sketch the regions associated
with your push and catch of the cart.
6. The gravitational potential energy (PE) of the cart depends on the height of the cart above the table top (or
other reference point). The motion detector measures the distance between the cart and the motion detector along
the track. Is there a FIXED relationship between these two quantities for YOUR set-up? If so, what is the
relationship between the two? If not, why not?
7. Sketch a prediction graph of the potential energy of the cart (the energy due to raising the cart's mass in the
gravitational field of the earth = mgh). Define the potential energy to be zero at the height at which the cart is
first pushed. When is the potential energy zero again? When is it a maximum? (Write your answers to the right
of the graph)
©1999-2001 Thornton, Sokoloff and Cummings
8. Change the height-time graph to display the PE of the cart as a function of time. (This is done by placing the
cursor tip over the word "height" on the y-axis of the graph and clicking the left mouse button. Uncheck
“height”-you may need to scroll down to find it- and check “Gravitational PE”.) Compare the actual graph of
the cart's gravitational potential energy to your prediction, and sketch the actual graph on your activity sheet.
9. Sketch your prediction of the total mechanical energy (the sum of the kinetic and potential energies) of the
cart over time as it moves. Describe in words (using complete sentences) the nature of the mechanical energy of
the cart after the push and before the catch ( is it increasing, decreasing….?). Describe in words the nature of the
mechanical energy of the cart during the push. Describe in words the nature of the mechanical energy during the
catch.
10. Change the distance-time graph to display the total mechanical energy of the cart as a function of time. (This
is done by placing the cursor tip over the word "distance" on the y-axis of the graph and clicking the left mouse
button. Uncheck “distance” and check “Mechanical Energy”.) Compare the actual graph of the cart's
mechanical energy to your prediction and sketch the correct graph now. Mark the push and catch on your sketch.
11. State in complete sentences the main differences in the graphs of the cart’s KE, Ug, and mechanical energy.
12. Explain what "conserved" means. Is the kinetic energy of the cart conserved? How do you know this? Is the
gravitational potential energy of the cart conserved? How do you know this? Is the mechanical energy
conserved? How do you know this?
13. Where does the cart get its initial energy? Where does the energy go at the end of the motion?
14. Consider a cart that is released from rest at the top of an incline and is allowed to roll to the bottom of the
incline with very little friction present. When the cart reaches the bottom of the incline, it has a speed of 10 m/s.
a) If the incline is made to be just as high but much longer, will the cart's speed at the bottom of the incline be
greater than 10 m/s? Less than 10 m/s? or 10 m/s? Explain why you chose the answer that you did (using
complete sentences).
b) If the incline is made to be just as high but much shorter, will the cart's speed at the bottom of the incline be
greater than 10 m/s? Less than 10 m/s? or 10 m/s? Explain why you chose the answer that you did (using
complete sentences).
c) If the incline is made to be just as long but much higher, will the cart's speed at the bottom of the incline be
greater than 10 m/s? Less than 10 m/s? or 10 m/s? Explain why you chose the answer that you did (using
complete sentences).
15. We often need to know the angle that an incline makes with a horizontal surface. Describe at least two ways
that one could determine the angle () that the track makes with the horizontal table top. How can we find sin 
without using a calculator or protractor?
16. We used the motion detector to measure the position of the cart on the track. The location of the motion
detector is chosen to be our origin. Can we use the data collected by the motion sensor and our knowledge of the
track's angle of inclination () to calculate the height of the cart above the tabletop? If so, how?
17. PE=mgh where h is the height above the starting point, g is the acceleration due to gravity, and m is the
mass of the cart. By using trigonometry we can calculate h from x, which is the distance of the cart from the
motion detector. Derive the expression for h in terms of x, xi (the initial position) and ø (the angle the track
makes with the horizontal)?
18. How would your graphs of Ug, KE and mechanical energy change if we chose a different point (one other
than the cart's initial height) to call our "zero height"?
©1999-2001 Thornton, Sokoloff and Cummings