15-Mar-2017: Lab 5 Trajectories

Lab 5: Trajectories
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date of lab performed: 15-March-2017

Purpose: The purpose of this experiment was to help us understand projectile motion and guide us to use calculations to predict the point where the ball will land.

Theory/ Introduction: We set up the apparatus so that we could find the velocity of the ball when it left the v-channel. We first found the position where the ball landed so that we could place the paper and carbon paper on its impact point and measure its position. We launched the ball 5 times in order to see if the ball landed on the same spot. We measured the height of the ball when it left the v-channel and the distance in the horizontal direction the ball traveled. We used our measurement of height and distance and found the launch speed of the ball. We also took to account the unpropagated uncertainty of our measurement tools (metric ruler has an uncertainty of 0.01 m).

Next, we attached an inclined board at the edge of the table and measured the angle at which the board is placed. This angle is used to find the x and y-component of the diagonal distance the ball hits the board. We then launched the ball so we know where the impact point is on the board. After attaching paper and carbon paper on the impact point of the board, we launched the ball 5 times to see if the ball lands on the same spot. We measured the diagonal distance the ball landed from the launch point. The reason why we needed this distance is because we compared the measured distance to the predicted distance that we calculated using kinematics.

Then, using the horizontal and vertical distance we calculated using the angle and the theoretical diagonal distance, we solved for the propagated uncertainty for the theoretical diagonal distance.

Summary:
First, we set up the apparatus like this.

We set a plumb bob in order to identify x=0m as well as determining the height.

After setting up the apparatus, we placed the ball on top of the inclined ramp (and made sure to put the ball on a place that can be easily identified as the starting point) and had a test run to see where to place the paper and carbon paper.

After we placed the paper and carbon paper, we ran the test five times. After the 5th trial, we lifted the carbon paper to measure the distance. 

After finishing our measurements, we attached a metal board to the edge of the lab table. We placed a weight at the end of the inclined board in order to keep it from moving. We then measured the angle the board is placed in.

We ran a test trial first to see the impact point of the ball. Once we attached the paper and carbon paper over the carbon paper, we ran 5 trials. After the 5th trial, we lifted the carbon paper to measure the distance from the v-channel (where the ball left) to the impact point.

Measured Data:

Distance (in the horizontal and vertical direction) the ball traveled

Height: 0.9430 plus or minus 0.0001 meters

Distance (horizontal direction): 0.9110 plus or minus 0.0001 meters

Diagonal distance the ball traveled (distance from end of V-channel to impact point on board)

=0.481 plus or minus 0.001 meters

Alpha = 24.6 plus or minus 0.1 degrees

Calculated Results:

Velocity of the ball when it leaves the V-channel

Calculated value of theoretical diagonal distance

Calculated propagated uncertainty of the theoretical diagonal distance

Explanation:
This is covered in the theory/ introduction section of the blog.

Conclusions: Although the theoretical diagonal distance was very similar to the experimental diagonal distance, they were not within their respective propagated uncertainty ranges. This error may have resulted from the inaccuracy of the angle measuring tool. When we used our phones to measure our angle, we gotten the different value from the value given by the angle measurement tool. Although we decided on using the angle given by the angle measurement tool, the phone may have given a more accurate value, resulting in error of results.