Partners: Sam Bachmeier, Hans Dittrich, Ryan Sokup Physics
Ryan Job
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 t he 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. t able.
Partners: Sam Bachmeier, Hans Dittrich, Ryan Sokup Physics
Ryan Job
Method: We had two balls, one wooden and the other metal. Each one w as 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)at 2 + V0t + Y0, we substituted 0m for Y (the ball ended up on
the ground, which is 0m), -9.81m/s 2 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 t hat 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 t ime. 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 r ise is m and the run is m/s. When W hen 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 t he only data point that was recor ded 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.
