Experiment 5: Conservation of Energy
The purpose is to verify that energy is conserved as a glider moves on an air track. The air track is
tipped by inserting a block of measured thickness under one end. The glider’s motion is recorded
by a computer attached to a sonic motion sensor, as in the F = ma lab. The results are displayed on
a velocity versus position graph. Two points through which the glider moves are chosen. The
energy of the glider-counterweight system at the initial point is compared to its energy at the final
point.
Procedure:
The apparatus is the same as in the F = ma lab, except that you will tilt the air track by placing a
metal block under one end.
Place the air track where the counterweight won’t hit the table, level it, check for friction, and check
the valve on the air pulley, as described in lab 3.
Measure T, the thickness of the block, using a vernier caliper as described in lab 1A. Measure the
distance, L, between the track's feet. (See picture, next page.) Measure the glider's mass, m1. Skip
determining uncertainties in these numbers. (Having you determine all of the uncertainties yourself
makes this lab too long. So, you will do the uncertainties in kinetic energy from scratch, but just
assume the potential energies are good + 5%. T and L go into the potential energies, and the
uncertainty in m1 is too small to worry about.)
Now, insert the metal block under the track's leveling screw (not the end with two screws). Attach
audio tape to the glider, pass it over the air pulley, and attach a small mass, m2, (20 or 25 g) to the
other end. Place the sensor about 45 cm from where you will release the glider, and get it aimed.
Refer back to lab 3, and repeat the same procedure to obtain a graph of the glider's speed vs. time.
Don't do the best fit line or print it out yet. Now,
a. Click time by the horizontal axis. On the menu, click Position (m). The graph now shows
speed as a function of position. Adjust the graph’s scale by dragging the numbers by the axes.
b. To get a best fit curve, click the triangle in
in the top toolbar. Select either an
inverse square fit or a quadratic fit, whichever gives the smaller RMS error. (vf2 = vi2 + 2ax
actually matches the form of the software’s power fit, but it seems to insist on the 4th power
when we need the ½ power.) Right now, it's trying to fit this curve to every point in the data
set. Click
. A box will appear on the graph. Get this box around the part of the graph
where the glider was gaining speed by dragging the sides of the box. Now it is fitting to just
these points instead.
This should be a region at least 50 cm long, hopefully more. If not, try to get better data,
perhaps with the instructor's help. The most common problem is a badly aimed motion sensor.
c. To save time, skip putting error bars on the graph. Print a copy of the graph. One copy per
group is enough. Don't exit from it yet.
Click on
. Drag the crosshairs to a point on the best fit curve near its start and read its
coordinates, xi and vi . Drag it to a point near the other end to read xf and vf. Again, the x values
should be at least 50 cm apart, hopefully more. Use RMSE from the box on the graph for the
uncertainty in m/s of both vi and vf. (That’s m/s not a percent.)
Calculations: Picture an x axis going along the
air track. You picked two points on it, i and f.
Your objective is to independently determine the
system's energy when the glider was at each
point, and compare.
1. Find s, the distance along the x axis between
points i and f. (Skip the uncertainty. Skip it in
steps 2-4 too.)
2. Find Δh1, the vertical distance the glider moves between points i and f. This is not just the
thickness of the block. Rather, notice that the two highlighted triangles are similar, and therefore
have the same ratio between their sides: Δh1/s = T/L.
3. What is Δh2, the vertical distance which the counterweight moves between these same two
instants?
4. Write down the initial and final heights for the glider and counterweight, based on Δh1 and Δh2.
(Recall that height can be measured from any convenient level. The simplest thing to do is to say
the lower of the two heights is zero, and the higher one is Δh.)
5. Determine the system's total initial energy by finding the kinetic and potential energies of both
objects, and adding them up. Reminder: v2 has twice the percent of uncertainty that v does. The
uncertainty in m is small enough to call zero. Assume the potential energies are good to + 5%.
Show how to set the calculations up in the space provided.
6. Repeat, using your final values to determine the final energy.
7. Within the uncertainty, does Ei = Ef?
PHY 131
Experiment 5: Conservation of Energy
L = _____________ T = _____________ m1 = ______________ m2 = ______________
Initially: xi = ___________
vi = ___________ + ___________
Finally: xf = ___________
vf = ___________ + ___________
Name of person whose paper has your group's graph: ________________________________
s = _____________
Δh1 = ______________
(Show calculation)
Δh2 = _______________
glider: hi = _______________ hf = _______________
weight: hi = _______________ hf = _______________
Compute Ei:
KE1 =
= ____________ + ___________ J
KE2 =
= ____________ + ___________ J
Ug1 =
= ____________ + ___________ J
Ug2 =
= ____________ + ___________ J
Total Ei = ____________ + ___________ J
Compute Ef:
KE1 =
= ____________ + ___________ J
KE2 =
= ____________ + ___________ J
Ug1 =
= ____________ + ___________ J
Ug2 =
= ____________ + ___________ J
Total Ef = ____________ + ___________ J