Properties of Projectiles

Overview:
We started a new unit with an introductory experiment. The experiment was simply to throw a ball forward and upward, and take a video. From there, we uploaded the video to a program called PascoCapstone. We tracked the ball's motion while in the air and then were able to find some key characteristics of projectile motion. The main thing that we discovered was that the motion in the horizontal direction is completely independent from the motion in the vertical direction.

Graphs/Raw Data:

This image shows the path of the ball that we threw. The red plus signs show the position of the ball. 

This graph shows the position of the ball vs the time. The red line is the horizontal displacement, and the green line is the vertical displacement.

This graph shows the velocity of the ball vs. the time. The pink line shows the velocity of the Y-axis. The blue line shows the velocity of the X-axis.

Analysis of Data:
With the information that these graphs have given, we can manipulate the data to find certain unknowns.

Acceleration in y axis: 9.8m/s^2 -- We know this because on earth the force of gravity is always the same.
Acceleration in x axis: 0 m/s^2 -- We know this because there is no unbalanced force to accelerate the ball in the horizontal direction. It is at constant velocity.

Initial velocity in y: ~2.1m/s -- We know this because its the y intercept of the vertical plane
Initial velocity in x: 3.88m/s -- We know this because it is the y-intercept for the horizontal plane

Velocity at the top of the path on y axis: 0m/s^2 -- We know this because the ball is changing direction and stops momentarily.
Velocity at the top of the path on x axis: 3.8m/s -- constant velocity

Final Velocity in x: 2.2 m/s -- final point on v vs. t graph
Final Velocity in y: -0.5m/s -- final point on v vs. t graph

How High the ball got: 2.53m -- we can look on the x vs. t graph
How far the ball went: 3.05m -- I used Xfinal - Xinitial = Change in X

Time for the ball to reach the top of its path: 0.835s -- Used equation Vf=at+Vi
Total air time for ball: 1.57s -- x=1/2at^2+vit

Conclusions:
In this experiment, we learned that the vertical and horizontal motions are completely unrelated when dealing with projectiles. We also discovered that all horizontal motion was constant, so we could use formulas and equations from the BFPM unit. The vertical motion was all constant acceleration; we used the UFPM equations. The same principle applied for solving for displacement. The horizontal motion remained constant for the entire trip and the vertical motion stopped at the top of the path. Furthermore, we were able to use the graphs that we created to find many of the unknowns, which proved to be helpful.

UFPM Practicum Lab

Goal:
The purpose of this lab was to test our knowledge of unbalanced forces and our applied use of kinematics. We demonstrated these skills with this lab. Our goal was to try and land a weight attached to a cart on another cart below going at constant velocity.

Procedure:
We first found the mass of the entire system. 0.693kg (We rounded to .64kg)

We then solved for acceleration. (The weight was .5N)

a=Fnet/m

a=.5N/.64kg

a=0.78m/s^2

After, we found the distance from the starting position of the weight to where it would land on the cart. The distance was .74m.

Using the information that we now had, we were able to solve using a formula for time.

x=1/2at^2+Vit

(.74)=1/2(.78)(t)^2

1.89=t^2

t=1.37s

Next, using the formula V=(change in)x/(change in)t we found the velocity of the cart on the ground. We concluded that the cart went 1 meter in 3.6 seconds. We manipulated these numbers to find that the cart had a constant velocity of .28m/s. Using these equations we hypothesized that if we placed the constant velocity cart 0.38m away from the weight. We could release both at the same time and the weight would land on top of the cart.

After our initial test, we proved our hypothesis correct and were able to land the weight perfectly on top of the cart.

We filmed our test which can be seen HERE.