15-Mar-2017: Trajectories

Lab 6: Trajectories
8-Mar-2017
Idea: Predict the impact point of a ball on an incline using projectile motion.

Summary: 
1) In regards to materials, we set up an incline connected to a ramp using a stand, a clamp, two metal v-channels, white+black carbon paper, and lastly, a steel ball. 

2) We then taped a sheet of paper with black carbon paper at approximately the spot where the steel ball would land, so the ball would leave a mark on the paper.

3) Next, we measured the height of the launch point, and released the ball five times.



4) Then, we measured how far from the edge the ball landed. The marks that our ball left on the carbon-paper were more or less consistent.



5) Using the height, I calculated the time it took for the ball to land. Then, I used the time and the measured distance to calculate the launch velocity of the ball.



6) Then, we propped an inclined wooden board right under the v-channel. Using the launch velocity I previously calculated, I set up an equation that would allow me to predict the landing point on the inclined board with α, the angle the board is at with respect to the ground. I attached the paper+carbon paper to the edge of the board



7) Then, after actually measuring α, I attached the paper+carbon paper to the edge of the board and again rolled the steel ball five times.



8) To get the uncertainty for this measurement, we made our measurement for x the middle mark, and our uncertainty was the range of the farthest and closest mark.

Analysis:

As I noticed early on with the first test case, the marks left by the carbon paper were surprisingly consistent. When solving for v0, I knew that the vertical component of the launch velocity would be zero, due to the horizontal launch ramp, which let me solve for time, which let me solve for v0 knowing the horizontal distance traveled in the first case. In addition, as all the measurements for height and length were done with a meter stick, they ha an uncertainty of around tenth to a fifth a centimeter.

When calculating/predicting the landing spot, I used the obtained v0, and our measured angle alpha and set the equations for distance for both the x and y directions:

Then, I actually did the second test and recorded the length, as already mentioned on step 8. As I could see, even with the uncertainty in mind, my prediction was off by 1-2 cm.

Conclusion:

In calculating my uncertainty, I had to take into account the uncertainty of my height+length measurements, alpha, and their subsequent calculations that give the values of time, and launch velocity.

Therefore, with a propagated uncertainty of distance of 6.82 cm, my calculated prediction was definitely more accurate than it could have been.