Download Conservation of Energy

Summer 2006
Conservation of Mechanical Energy (Projectile Gun)
Name
Section
Theory
In an isolated system subject only to a conservative force, it can be shown that the mechanical energy of the system remains
constant. In other words, the sum of the kinetic energy K and potential energy U is constant for the system.
K + U = E (constant )
(1)
This force could be gravitational, elastic, or electromagnetic in nature. In any case, the total energy of the system will remain
constant. As you can see from Equation 1, as one form of energy decreases, the other must increase by the same amount.
In this experiment, we will examine the energy of a sphere projected vertically; i.e., subject only to the gravitational force. We
define the potential energy at the release point to be 0 so that the sphere has only a kinetic energy dependent upon its initial
velocity. As the sphere rises, its potential energy increases as its kinetic energy decreases.
Apparatus
Pasco Mini Launcher, Clamp, Steel sphere, Paper, Carbon paper, Tape, Plumb bob, Meterstick, Triple-beam balance.
Procedure
1. Determine the initial velocity of the sphere. Clamp the gun apparatus to the side of the table and set the gun to shoot
horizontally as shown in the figure.
2. Tape a sheet of paper on the floor under the gun so that the
release point of the sphere (shown on the side of the gun)
can be transferred to the floor. The plumb bob will help
with this.
3. Fire a test shot from the gun at medium range and note
where the sphere strikes the floor. Tape another sheet of
paper at this location and place a sheet of carbon paper on
top.
4. Fire 10 shots from the gun onto the target paper.
5. Remove the carbon paper and measure the horizontal distance x each of the shots traveled form the point you marked on
the floor under the gun. Record these values in Table 1 and calculate the average distance and average deviation in distance.
6. Measure the vertical distance y the sphere (freely) falls from the gun to the floor. Use this distance to calculate how long the
sphere is in the air.
y=
1 2
gt
2
(2)
7. Each shot was in the air the same amount of time. Since the horizontal distance varied, this means that there was some
variation in the initial velocity of the sphere. Calculate three initial velocities – one from the average distance, one from the
minimum distance (average - deviation), and one from the maximum distance (average + deviation). There is no force on the
sphere in the horizontal direction, so the horizontal velocity (also the initial velocity of the sphere since it was fired
horizontally) is constant.
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v=
x
t
(3)
Re-record these velocities as (average ± deviation). Finally, express this deviation as a percentage of the mean.
8. Measure the mass of the sphere with the triple-beam balance. Calculate the kinetic energy of the sphere as it leaves the gun
(three values).
K=
1
mv 2
2
(4)
Re-record this kinetic energy as (average ± deviation), and express the deviation as a percentage of the mean.
9. Assuming that mechanical energy is conserved, calculate the expected vertical distance h the sphere will travel when shot
vertically from the gun as shown in the figure (three values).
U = mgh
(5)
You now have a range of vertical distances the sphere could travel, based on the
uncertainty in the initial velocity.
10. These calculated distances are from the release point, but you need to know how high
off the floor it will rise. Measure the distance from the release point to the floor and add
this to your high and low distances. Mark the high and low expected vertical distances
you determined on the 2m meterstick with some tape.
11. Hold the meterstick vertically next to the gun and fire the sphere straight up. Watch and
see if the sphere ascends to within this range.
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Table 1
Data and Calculations
Horizontal Distances x (m)
Average distance (m) ____________________
Average deviation (m) ____________________
Freefall distance y (m) ____________________
Freefall time t (s) ____________________
Mass of sphere (kg) ____________________
Minimum velocity (m/s) ____________________
Minimum kinetic energy (J) ____________________
Average velocity (m/s) ____________________
Average kinetic energy (J) ____________________
Maximum velocity (m/s) ____________________
Maximum kinetic energy (J) ____________________
Velocity
Kinetic Energy
( _______________ ± __________ ) m/s
( _______________ ± __________ ) J
Deviation as percentage of mean ____________
Deviation as percentage of mean ____________
Distance from release point to floor (m) ____________________
Minimum height from gun (m) ____________________
Maximum height from gun (m) ____________________
Minimum height from floor (m) ____________________
Maximum height from floor (m) ____________________
Did your vertical shot fall within the predicted range? _______________
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Questions
1. You calculated a deviation as a percentage of the mean for both initial velocity and kinetic energy. How do these percentages
compare? Why do you think this is so?
2. Consider the gun – sphere system. In order to shoot the sphere, you cock the gun by compressing the spring inside. If
mechanical energy is conserved for this system, what do you think the elastic potential energy is in the spring when the gun is
set to shoot on medium range? Give a numerical value.
3. We defined the potential energy of the sphere at the point of release to be 0. Was this necessary? Could we have taken the
point of 0 potential to be the floor under the gun? Would mechanical energy still be conserved in this case?
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Pre-Lab: Conservation of Mechanical Energy (Projectile Gun)
Name
Section
1. What is the conservation of mechanical energy?
2. Calculate the average and average deviation in the following values. Express your answer in the form
( average ± deviation ) units
Finally, express the deviation as a percentage of the mean (a single percentage value).
Distance
(cm)
68.9
72.1
72.3
68.3
70.5
71.0
69.4
71.9
69.3
70.7
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