Download CONSERVATION OF MECHANICAL ENERGY (40 minutes) Exp

CONSERVATION OF MECHANICAL ENERGY
(40 minutes)
Exp. #14
Name: _____________________ Partners: _______________________Section No. _______
(Alward File: "c:\textbook\Conserve.Doc" 2-16-04)
Equipment Needed:
Pasco Signal Interface Cylindrical Weight (100-300 grams)
2 meter pole Blue Clamp Utility Clamp
45-cm Crossbar 130-cm String
Photogate + stand Vernier Caliper 5'' Masking tape for each table Meter stick
PURPOSE AND THEORY
In this exercise the student will verify that the total mechanical energy of a system is conserved,
provided that the only forces doing work are conservative forces. Our system will be a particle swinging
at the end of a string. Two forces act on the mass: Tension T, and weight W. Since T is always
perpendicular to the direction of motion, it does no work. The other force, W, is a conservative force,
which means that work done by this force does not change the total energy of the particle.
The total energy E of this particle is defined according to the expression given in Equation 1. The term
mgh is called the gravitational potential energy, and h is the altitude (elevation) of the particle with
respect to any arbitrarily chosen reference "ground".
Equation 2 expresses the fact that the sum of the gravitational potential energy and the kinetic energy at
one instant, is equal to the same sum at some later instant. Thus, this sum (the total energy) is
conserved; in other words, it remains constant.
E = mgh + ½ mv2
(1)
mgh1 + ½ mv12 = mgh2 + ½ mv22
(2)
PROCEDURE
These steps may be skipped if the Science Workshop interface screen is already
on the screen, including a digital display window for velocity data.
1. Turn on the signal interface, then turn on the computer.
2. Connect the photogate’s plug into Digital Channel 1 on the interface.
3. From the File pull-down menu, Open the file named “Conserve.Sws”.
The hanging mass will be suspended from a crossbar attached to a support stand at the edge of the table.
The mass will be pulled to the side and released from some pre-determined height h1 above the floor.
As the mass passes through it lowest point (at some known elevation h2), its speed will be measured. In
this manner, the experimenter will know the initial and final values of the elevation and speed of the
mass, and will use these values to verify Equation 2.
4. Place the photogate assembly on the floor and place the stand with crossbar at the edge of the table.
5. Measure the diameter of the cylinder and its mass. Because the first 1.5 mm of the cylinder is used to
completely block the photogate beam, the effective diameter is 0.0015 m smaller than the actual
diameter; subtract 0.0015 m from the actual diameter and record the effective diameter in the table
below; record the mass, also.
6. Attach a string of length 1.0 to 1.5 meters long to the crossbar. At the end of the string hang a
cylindrical object of mass m not less than 100 grams and not greater than 300 grams. Make sure that the
cylinder is capable of fully blocking the photogate’s infra-red beam when it is hanging stationary inside
the photogate. It is not necessary to adjust the length of the string; just raise or lower the photogate.
TABLE 1: THE CYLINDER
Mass:
m=
kg
Diameter:
d=
m
(Effective diameter corrected for
beam width.)
2
7. Calibrate the photogate. The speed of the swinging mass as it passes through the photogate beam is
calculated by dividing the diameter of the cylinder by the travel time through the beam. This calculation
is done by the computer software, but first it must be told the diameter of the cylinder. Do this now.
Click on the photogate icon (see the arrow in the figure below). This will open up the Photogate Setup
window.
In the Object Length box, enter the effective diameter (< 0.050 m) of the cylinder, then click OK.
8. Measure the elevation h2 at bottom of swing.
9. Release the mass from rest from the elevations h1 shown in the table. Speed data is
generated and displayed on a digital display panel on the monitor screen. Catch the swinging mass after
its first pass through the photogate and place it on the table. Release the mass four times to collect four
velocities (they will be approximately the same); average these velocities.
10. Using the average velocity, calculate the kinetic energy KE2 when the mass is at its lowest elevation
h2 and add it to the calculated value of the gravitational potential energy PE2 at that elevation. This is
the total energy E2. Also calculate the total energy E1 of the mass when it was released from rest at the
higher elevation. These two total energies should be about equal.
11. Calculate the percentage difference between the initial total energy E1 and the final total energy E2:
divide the absolute value of the difference by the initial energy, and multiply by 100.
3
Kinetic Energy, Gravitational Potential Energy, and Total Energy for a Mass m =
Trial 1
h1
0.60
Trial 2
m
0.50
kg
Trial 3
m
0.40
m
h2
Velocities v2
Trial 1
Velocities v2
m/s
Velocities v2
m/s
m/s
Trial 2
m/s
m/s
m/s
Trial 3
m/s
m/s
m/s
Trial 4
m/s
m/s
m/s
Average:
m/s
m/s
m/s
KE2 = ½ mv22
J
J
J
PE2 = mgh2
J
J
J
E2 = KE2 + PE2
J
J
J
KE1 = ½ mv12
0.00
J
0.00
J
0.00
J
PE1 = mgh1
J
J
J
E1 = KE1 + PE1
J
J
J
Percent Difference
%
%
%
|E2 - E1| x 100%/E1
4