Download CONSERVATION OF ENERGY

Physics 211 Experiment #7 CONSERVATION OF ENERGY
Pre-Lab Assignment
1. Read the lab instructions.
2. A hanging mass of 1500 grams compresses a spring 2.0 cm. Find the spring
constant in N/m.
3. The spring is compressed a total of 3.0 cm, and used to set a 500 gram cart into
motion. Find the speed of the cart at the instant it is released, assuming all the elastic
potential energy is converted to kinetic energy.
4. Suppose the cart is on a track that is elevated at one end. Find the maximum
height h above the plane of the tabletop that the cart will rise to before coming to a
stop; assume that all the kinetic energy is converted to gravitational potential energy.
Apparatus
Pasco 750 Interface
1.2 meter dynamics track, and a spirit level
From track accessories: 1 adjustable end-stop, and 1 track support
Three-hole pulley on a rod
Universal clamp
Dynamic cart (with plunger and weight)
Photogate head with mounting bracket and five-pattern picket fence
Meter-stick, table clamp
O-Haus triple beam mass balance
1 inch by ¼ inch bolt, nut, and washers to attach to adjustable end-stop
Theory
If a mechanical process takes place without losses to friction or other dissipative force,
the energy of the system is conserved. This means that the energy can be transformed
without loss from one form of mechanical energy to another, such as elastic potential
energy to kinetic energy, or kinetic energy to gravitational potential energy, for
example. If friction is present, some or all of the energy is converted into heat, which
is another form of energy.
Three forms of mechanical energy are involved in this experiment:
(1)
Kinetic Energy = K = ½ m v2
(2)
Gravitational Potential Energy = Ugr = mgh
(3)
Elastic Potential Energy = Uel = ½ kx2
In the last expression k is the spring constant, which applies to a spring that obeys
Hooke’s Law, F = -kx, where a force F causes the spring to be compressed or elongated
a distance x away from its equilibrium position.
If a compressed spring is used to accelerate an object and all of the elastic potential
energy is transferred to the object, then ½ kx2 = ½ mv2.
If the object rises until it stops, in the absence of friction, the kinetic energy will all be
converted to gravitational potential energy, so ½ mv2 = mgh, where h is the change in
height of the object.
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Description of Experiment, and Objectives
In this experiment you will:
(A) measure the spring constant of a spring, and measure the elastic potential
energy stored in this spring when it is compressed,
(B) measure the kinetic energy of a cart that is released from the compressed
spring,
(C) measure the maximum height that the cart achieves, and
(D) compare the results obtained in parts (A) and (B), parts (A) and (C), and parts
(B) and (C).
The experiment uses a dynamic cart with a spring-loaded plunger. First the spring
constant is found by taking data on the spring force and compression distance.
The spring is then used to fire the cart along a horizontal track. The velocity of the
cart is measured by using a photogate and “picket fence.” The kinetic energy of the
cart will be compared with the elastic potential energy stored in the spring. This
comparison will be used to determined whether all the elastic potential energy was
converted to kinetic energy.
Finally, the spring fires the cart up an inclined track, and the change of height is
measured. This tests whether the kinetic energy is all converted to gravitational
potential energy.
Figure 1. Equipment set up to measure the spring constant.
Procedure
A. Measurement of Spring Constant for Determination of the Potential Energy of
a Compressed Spring
I. Set up the apparatus as shown in Figure 1.
1. Place the track at the end of the lab table. Using the spirit level, adjust the
bolt in the permanent end-stop to level the track.
2. DO NOT CLAMP THE TRACK TO THE TABLE. Attach the pulley tothe end of
the track using the clamp.
3. Attach an adjustable end-stop as shown, with a 1 inch by ¼ inch bolt, nut,
and washers for the spring-loaded plunger to push against.
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4. Place the dynamic cart on the track. Tie a string from the small hole above
the plunger and lead it over the pulley to a 50 gram mass holder.
5. Add 150 more grams to the mass holder, making a total of 200 grams. Read
the centimeter scale reading at the left end of the cart and record it.
6. Add 200 grams to the load and again read and record the scale at the left
end of the cart.
7. Continue to add 200 grams at a time and record the scale readings. If you
notice that friction causes a spread of possible readings for any load,
choose the reading at the center of that spread. Continue until the total
load is 1800 grams.
II. Calculate the spring constant as follows (see example below)
1. Convert the load values to kilograms and multiply by g = 9.8 m/s2 to obtain
the weight in Newtons. This weight is equal to the magnitude of the spring
force.
2. Convert the scale readings to meters.
3. Using Excel, plot the values of spring force versus the scale readings; the
scale readings must be on the x-axis (see the example given below). Use
chart wizard to plot the graph and to draw a linear trendline. Display the
equation of the best-fit straight line on the graph, and print the graph. The
coefficient of x in the graph is the spring constant. Record the spring
constant.
Figure 2. Track set up to measure the velocity of the cart after spring release.
B. Measurement of Cart Velocity after Spring Release for Determination of the
Kinetic Energy of the Cart
In this part of the experiment the elastic potential energy stored in the spring will
be converted to the kinetic energy of the cart (or cart plus mass). We will measure
the velocity of the cart, determine the kinetic energy of the cart, and compare this
with the elastic potential energy initially stored in the spring. Thus, in addition to
the speed and mass of the cart, you will need to compute and record the initial
potential energy stored in the spring.
I. Set up the apparatus as shown in Figure 2 to measure the velocity of the cart
after spring release.
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1.
Place the track on the table so that the permanent end-stop is away from
the computer. Level the track with the spirit level, using the bolt in the endstop.
2. DO NOT CLAMP THE TRACK TO THE TABLE. Just attach the heavy-duty
table clamp to the table end near the computer, and push the track up
against it.
3. Attach the adjustable end-stop about 10 centimeters from the end of the
track near the computer. This end-stop should still have the 1 inch by ¼
inch bolt with nut and washers attached for the plunger to push on.
4. Place the dynamics cart on the track as shown with the plunger touching
only the bolt described in step 3. Put the five-pattern picket fence in the
cart, with the closest interval pattern on top. (In that pattern each light and
dark band is .5 centimeters wide.)
5. Attach the photogate to the track using its mounting bracket, about 5 cm
beyond the cart. Adjust its height so that the light beam passes through the
close interval pattern of the picket fence. Plug its cable into digital channel
1 of the interface.
6. Weigh the dynamics cart (with picket fence on it.) Also weigh the black
rectangular metal bar to be used as a load in the cart.
7. With the plunger not compressed, place the cart on the track with the
plunger touching the bolt, and read the position of the end of the cart.
Repeat this with the plunger locked in the most compressed position.
Subtract to find the distance (x) the spring is compressed.
II. Set up the interface and computer as follows:
1. Turn on the computer interface box, login to the computer, and open Data
Studio.
2. Drag the digital plug to digital channel 1. From the list of sensors, choose
Photogate and Picket Fence.
3. Double-click on the picket fence icon to get the picket fence sensor
properties window. Under measurement, de-select acceleration and velocity
so that only position is selected. Click on constant, and change the band
spacing to 0.01m.
4. Set up a graph.
III. To take a velocity measurement proceed as follows (Steps 1 to 10).
1. Move the track so that it pushes up against the table clamp.
2. Compress the plunger spring on the dynamic cart all the way in and latch
it in the innermost position.
3. Place the cart on the track with the plunger touching the bolt on the endstop.
4. Click on “start."
5. Release the spring by lightly tapping the spring release with a rigid object.
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6. After the cart passes the photogate, click on “Stop.
7. Select 'scale to fit.'
8. Choose a linear fit. The slope is equal to the velocity. Record the velocity
into an excel spreadsheet.
IV. Measure the velocity at least five times (by doing steps 1 to 10 above.) Average
the three highest values.
V. Place the rectangular metal weight in the cart, and measure the velocity after
release eight times. Average the three highest values.
Figure 3. Equipment set up to measure the height the cart rises after spring release.
C. Measurement of Cart Elevation After Spring Release to Determine the
Gravitational Potential Energy
In this part of the experiment, the elastic potential energy of the spring is converted
into the kinetic energy of the cart and any mass the cart carries, which is then
converted into gravitational potential energy. You will measure the change in the
height of the cart, compute the change in gravitational potential energy, and compare
this with the initial elastic potential energy, and the kinetic energy of the cart when it
moved on a horizontal surface.
I. Set up the apparatus as shown in Figure 3.
1. Leave the table clamp in place from part B of this experiment.
2. Attach a Pasco track support at the 1 centimeter mark and adjust its two
bolts so that the bottom of the track is a distance d above the lab table;
measure and record d. Use basic geometry to determine the angle  the
track makes with the tabletop.
3. Attach the adjustable stop that the plunger pushes against to the lower end
of the track.
II.
To measure the distance traveled uphill by the cart.
1. Compress the plunger all the way in and latch it in the innermost
position.
2. Place the cart on the track with the plunger resting against the bolt.
3. Record the initial scale reading at the high end of the cart.
4. Tap the spring release lightly with a metal bar.
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5. As the cart rolls up the track, record the highest scale reading reached
by the front of the cart.
III. Measurements to be taken:
1. Remove the load block, but with the cart still holding the picket fence, follow
steps 1 to 5 above to measure the highest scale reading five times. Average
the three highest values, and record the average. Subtract the initial scale
reading to find the distance L traveled along the track. Use this length L,
and the angle  determined in part I.2. to find the change in the height of
the cart, h.
2. Repeat step 1, but with the mass load in the cart.
Calculations
1. Calculate the elastic potential energy in the spring when the spring is latched in the
most compressed position. Use the spring constant found in part A, and the maximum
compression distance found in parts B.
2. Calculate the kinetic energy of the cart (and picket fence) after it is fired by the spring.
Use the mass and velocity values found in B. Compare this with the elastic potential
energy in the spring. What percent of elastic energy was not converted to kinetic
energy?
3. Repeat calculation 2 for the cart containing the mass load (and picket fence.)
4. Calculate the gain of gravitational potential energy for the cart (and picket fence), using
the change in elevation from part C. Compare this with the kinetic energy from
calculation 2, and with the elastic potential energy from calculation 1.
5. Repeat calculation 4 for the cart containing the mass load (and picket fence.)
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