Lab 8 Report
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Lab 8 Report
PI: Isaac Madill
DA: Luke Katalinic
Introduction
The goal of this experiment was to calculate the speed of a ball fired out of a projectile launcher
using two different methods. One method used involved taking measurements of the final angle
of the pendulum, the radius of the pendulum, as well as mass of the ball and pendulum. Using
some basic equations to calculate the change in height, gravitational potential energy, and
velocity of the pendulum and ball together, the researchers were able to isolate the velocity of the
ball. For the other method used, the researchers calculated the velocity of the ball by gathering
data from how far the ball was launched in a linear direction from a constant height. A piece of
paper towel was used to identify exactly where the ball landed as the ball left an imprint. Both
methods yielded sperate velocities respectively.
Data Analysis – Method 1
Speaking on the systematic uncertainties of the first method when referring to the center of mass,
if a wrong center of mass is picked, then the overall height change will be consistently incorrect.
This is due to an incorrect measurement of the radius of the pendulum. This could cause a very
large uncertainty if not properly measured.
0
1
2
3
4
5
6
7
0
2
4
6
8
10
12
Velocity V. Trial
Ball Velocity
Pendulum-Ball Velocity
Trial
Velocity
v pendulum
v ball (m/s)
ball (m/s)
0.46924538
5
2.154262903
0.46924538
5
2.154262903
0.46924538
5
2.154262903
0.45467237
1
2.087359522
0.46924538
5
2.154262903
Data Analysis – Method 2
As for the second method, systematic uncertainty can be seen to exist in the measurement of the
height of the launch position. To solve the velocity of the second system we set the initial energy
equal to the final energy. The initial energy is all potential and the final energy is all kinetic. The
initial energy is equal to mass times acceleration due to gravity times the height, or mgh. The
final energy is one half times the mass times the velocity squared, or 1/2mv^2. Setting these two
equal we get that velocity is equal to the square root of two times the acceleration due to gravity
times the height. The way we solved for velocity was using distance traveled over time elapsed
and since we know the initial height, we know the time elapsed and can observe the distance
traveled we solve for velocity this way.
0
2
4
6
8
10
12
0
2
4
6
8
10
12
Method 1 v Method 2 Velocity
Method 1
Method 2
Trial
Velocity (m/s)
v ball (m/s)
6.443284877
6.513320582
6.548338434
6.583356287
6.600865213
Conclusion
As you can see in the graph for method one, the velocity of the ball is significantly
greater than the velocity of the pendulum. This is consistent with the idea that
momentum is conserved throughout the system. So, the total of the masses times
their respective velocities of the initial components of the system must be equal to
the total of the new total mass times its resulting velocity. In this graph you can
also see that our data is very consistent with itself, and this points to sound
experimental design with few uncertainties. This graph points to and agrees with
the idea that the velocity of the ball can be found through the ideas of conservation
of momentum.
In method two the idea was to use the initial potential energy and set it equal to the
final kinetic energy and solve for velocity this way but then it made more sense to
use the kinematic equations to solve for the time of the projectile and observe the
distance traveled and then use displacement over time. This method is also very
consistent with itself, but the two methods resulted in different velocities. Both
methods use the ideas of conservation of momentum and conservation of energy.
Group questions:
1. ) Yes the ball should be inside the pendulum for this measurement because when
we are actually observing the momentum of the pendulum the ball is inside of it, so
its mass should be considered.
2.) This could significantly impact the measurement of delta H because it moves
the center of mass of the pendulum down significantly, which is used directly in
the calculation of delta H.
3.) No, a significant amount of energy is lost to things like sound, and friction of
the collision which often produces small amounts of heat.
4.) This momentum is also transferred out of our observed system in the form of
things like heat and sound that come as a byproduct of friction. Because this is not
a perfect ideal collision.
5.) We attempted to measure our height of the ball which determines the initial
energy of the ball carefully but the measurement could have resulted in some
uncertainty. Another way we attempted to reduce uncertainty was through
clamping the launching system down, however we did not do this in method one.
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ACTIVITY 3
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The 0.20 kg puck on the frictionless, horizontal table in
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HA
Figure
1 of 1
X•10n
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1.20 kg
《圓
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