Lab 6 Trajectories

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 19 September 2016 

Trajectories

Mission Statement:To use my understanding of projectile motion to predict the impact point of a ball on an inclined board. 

Theory: Through experimentation, we were supposed to confirm the effectiveness of the kinematic equations which we were taught previously and see for ourselves just how effectively they model reality under relatively controlled circumstances with negligible air resistance.
Experimental Procedure for Part 1:
For this lab, we set up an apparatus depicted in the image below

Lifting the ring stand onto the table and then securing it to the table with a C-clamp, we proceeded to adjust a aluminum v-channel diagonally onto the ring stand with a specialized clamp, taking care to measure the angle between the v-channel and the table, shown below.

Then, off on the ground, we positioned a piece of carbon paper with tape, shown below

 Next, we rolled the ball down the v-channel five different times, each time releasing from the same position within the v-channel. We observed how the ball landed in nearly the same spot each time. Next, we proceeded to measure the height of the table, together with the distance from the table the ball landed in order to calculate the anticipated landing spot of the steel ball and the approximate launch speed. Furthermore, we likewise documented the uncertainty of our height and distance measurements, shown below.
Lists/Tables/Graphs of Collected Data with Explanation for Part 1:

From the information and calculations shown above, we showed the different horizontal distances the ball covered together with their uncertainties, followed by calculating the median distance of 0.7248 meters, which in turn is inputted into our standard kinematic equation, with the ratio between the horizontal distance covered and the desired initial velocity being substituted for time.When we solved for this desired initial horizontal velocity, we obtained a reasonable value of 1.66 m/s.
Experimental Procedure for Part 1:
Next, we slightly modified the experiment, depicted below. 

This time we were supposed to place a wooden plank diagonally, resting it against the edge of the table, setting up our apparatus to determine the distance d the steel ball will be covering under the same circumstances as the previous part, with the carbon paper wrapped around the wooden plank where we anticipated the ball would hit. Below is our set up. 

 First, we were first supposed to symbolically solve for d, then calculate it, then conduct the experiment five times in order to determine our experimental value for d, shown below.

Lists/Tables/Graphs of Collected Data with Explanation for Part 2:

From our work above, we see that, symbolically, d = (2sin(theta)*(V_0)^2)/(g*(cos(theta))^2)

Furthermore, when we carried out the calculation, we see that our calculated value of d is 0.72 plus/minus 0.1 meters, which is remarkably close to the 0.7248 meters we measured to be the horizontal distance covered by the steel ball during the first part of our experiment. 

Conclusion- Interestingly enough, our experimental values and calculated values were very close with minimal uncertainty. This is most likely due to the relative mechanical simplicity of the system, reducing the likelihood of error. Thus, we confirmed the effectiveness of the kinematic equations for modeling projectile motion.