Projectile Motion
Objective: This lab had several objectives. First, it showed the relationship between initial
velocity and
final position. Second, it showed that mass has no effect on velocity or position. Finally, it
showed that
horizontal velocity does not affect vertical velocity.
Setup: A ramp was placed on a table with two photo-gates placed at the end of the table. They
were
connected to a computer running Vernier Graphical Analysis, which measured the average
velocity of
the ball when it passed through both photo gates. There was a piece of tape on the floor to mark
the
edge of the table on the floor. There was a large piece of paper with a carbon sheet on the floor
as well.
After running all the trials for one type of ball, we measured how far out the ball was from the
table.
Partners: Sam Bachmeier, Hans Dittrich, Ryan Sokup
Physics
Ryan Job
Method: We had two balls, one wooden and the other metal. Each one was rolled down the
ramp ten
times. Each time it went down the ramp, through the two photo gates, and landed on the carbon
paper,
making a mark on the white paper underneath.
Data: We measured the table to be 0.92m up off the ground
Trial Velocity (m/s) Actual Distance (m) Expected Distance (m) Difference (m)
Metal 1
0.793
0.316
0.343
0.027
2
1.159
0.466
0.502
0.036
3
0.976
0.390
0.423
0.033
4
0.928
0.365
0.402
0.037
5
1.110
0.448
0.481
0.033
6
0.803
0.315
0.348
0.033
7
0.514
0.199
0.223
0.024
8
0.917
0.371
0.397
0.026
9
1.129
0.460
0.489
0.029
10
0.893
0.362
0.387
0.025
Wood 1
1.072
0.429
0.464
0.035
2
1.079
0.427
0.467
0.040
3
0.914
0.419
0.396
-0.023
4
0.791
0.309
0.343
0.034
5
0.508
0.187
0.220
0.033
6
0.949
0.385
0.411
0.026
7
1.036
0.420
0.449
0.029
8
0.751
0.289
0.325
0.036
9
0.519
0.192
0.225
0.033
10
0.652
0.241
0.282
0.041
Average Difference
0.02935
W/O Outlier
0.03211
Partners: Sam Bachmeier, Hans Dittrich, Ryan Sokup
Physics
Ryan Job
Calculations: Using the equation Y = (1/2)at2 + V0t + Y0, we substituted 0m for Y (the ball
ended up on
the ground, which is 0m), -9.81m/s2 for a (gravity), 0 for V0 (there was no initial vertical
velocity), and
0.92m for Y0 (the ball started 0.92m above the ground). Solving for t, we found that the ball was
in the
air for (1.84/9.81)1/2 seconds. Then, using the equation X = (1/2)at2 + V0t + X0, we substituted
0 for a
(there was no horizontal acceleration), (1.84/9.81)1/2seconds (about 0.433s) for t (how long the
ball was
in the air), and 0 for X0 (this was the edge of the table). Then we substituted the velocity
measured by
the photo gate for V0 and solved for X to find out how far the ball should have gone under
perfect
conditions (no air resistance, all velocity is forward, etc.). Finally, we subtracted the measured
distance
from the expected distance. All of these were then averaged, resulting in an average of 0.029m
(2.9cm)
greater expected value than measured value.
Conclusion: The equation that we used to calculate how long the ball was in the air shows that
the mass
and horizontal velocity do not affect how long the ball is in the air. Likewise, vertical acceleration
does
not affect the horizontal velocity, except when it causes the ball to hit the ground.
The equation that we used to calculate the distance the ball went shows that, when the ball has
no
acceleration and the initial position is 0, the only thing that affects it is the initial velocity and
time. This
means that vertical velocity and acceleration do not affect the horizontal velocity, apart from the
ball
hitting the ground. This is shown especially in the graph, as the time the ball was in the air,
0.433s, is
very close to the slope of the graph, 0.418. This makes sense, as slope is rise/run. In this case,
the rise is
m and the run is m/s. When divided, the result is just s, meaning the slope of the line is 0.418s.
All of these conclusions are supported by the data, as all but one of the points of data are very
close to
the expected value. In fact, all but the one data point are very close together. The average of
the
difference is 2.9cm with the outlier and 3.2cm without the outlier. This means that air resistance
and
friction from the table caused the ball to not travel about 3.2cm as far as expected. It is safe to
remove
the outlier from this calculation as it is the only data point that was recorded to go farther than
expected. The direction that the ball came out of the photo gates does not affect the horizontal
distance
because the photo gates and Vernier Graphical Analysis only measures the average horizontal
velocity of
the ball.