14-Sep-2016: Lab 5 Trajectories

1. Title: Lab 5 Trajectories
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 14-Sep-2016

2. Purpose
In this lab, to use our understanding of projectile motion to predict the impact point of a ball on an inclined board.

3. Theory/Introduction
When an object be a projectile, it will have a trajectory. Trajectory is the path that a moving object follows through space as a function of time. When the ball has a motion in projectile, we can observe when and where the ball land and we can find the horizontal and vertical distance from start point to the end point.

4. Apparatus/Experimental Produce
We set up the apparatus as below shown. Then, we launched the ball from a readily identifiable and repeatable point near the middle of the inclined ramp because we did not want the ball hit the ground to far away. After that, we released the ball in the middle of the inclined ramp in order to know where the ball landed.

Part 1
We taped a piece of carbon paper on the ground around where the ball landed. Launched the ball five times from the same place as before and verify that the ball lands in virtually the same place. Measured the height of the bottom of the ball when it launched, and measured how far out from the lab table's edge it landed.

Part 2
We set up this part in the same way, except we placed a board such that it touched the end of the lab table and the floor. We put a heavy mass on the ground at the foot of the board and use duct tape to fix the mass in place.The board and the ground provided an angle of theta. We got the angle of theta by iPhone compact function. In this time, we released the ball five times on the board on the same place instead of the ground. So, we taped the carbon paper on the board where the ball landed.

5. Data
In Part 1, We measured that distances by hang a plumb bob in order to get the distance accurately.

In part 2, we got five distances that how far the ball landed on the board from the table's edge.The angle theta is 50 degree, measured by iPhone.

6. Calculated Result
we need to determine the value of d by given v0 and a, here is the expression of d and the distances x.

7. Explanation of graph/Analysis

Through the equation of distance d, we got the theoretical value of d is 66.3+/0.01. 

Compare the experimental values for d, we got the experimental value of d by the average of five distances. Then, used the theoretical and experimental values to get the error percent in this lab experience. The error percent is 6.06%.

8.Conclusion
Through this lab experience, we studied how to use projectile motion to find the impact point of in inclined place. When ball was released from the top to the inclined place, we can get the distance by given the initial velocity and the angle between horizontal to the incline place. We had uncertainty and error in the experiment, the error percent is 6.06. The reason of causing error are the air assistance and the friction between the ball and the Aluminum "V-channel".