September 14, 2016: Trajectories (Projectile Motion)

Anthony Betancourt
Lab Partner: Josh Fofrich
Professor Wolf

Lab #5: Trajectories

Purpose:  The purpose of this lab is to predict the impact of a projectile on an incline board with the understanding of kinematics in 2 dimensional motion.  

Procedure:  

1. First set up the apparatus as shown on your lab table:
2. 
3. Pick a point on the inclined V-channel to launch the ball from.  Use this launch point for each trial.  
4. Practice launching ball off the edge of the table and notice where it lands.  Place a piece of white paper and carbon paper (carbon side down, white sheet underneath) in the area where the ball lands.
5. Launch the ball 5 times from the same position on the ramp.  Verify that the ball lands in the same area after each launch trial.
6. Determine the height of the bottom of the ball when it leaves the track and the distance it travels from the tables edge.  Determine launch speed of the ball from your measurements.  
7. Place a board on an incline under the path of the balls trajectory, such that the ball will strike it when launched from the same spot.  
8. Use smartphone to measure the incline of the board. Derive an expression that will determine the value of d along the board.  
9. Repeat experiment 5 times launching the ball from the same spot.  

Measured Data:

(Height from where ball launches; uncertainty in ∆x; launch speed)

(expression for d along the board)

Calculated Results:

(values for calculations above; d= 0.31m; h= 0.94m ± 0.005m; V= .97m/s)

(experimental value for d)

(Theoretical value of d)

Analysis: Once the height of the ball was determined, the velocity of the ball as it leaves the track was able to be calculated from the measurements made.  The calculations are shown above in the first photo.  Once the launch speed was calculated, it was applied to the second part of the experiment where d was determined along the incline of the board.  d is the distance the ball travels before hitting the inclined board.  Calculations showing the theoretical value of d are in the last two pictures.

Conclusion:  This experiment was simple but still has inherit uncertainty in the gather-able data.  The initial height calculated has some uncertainty due the measurement is reliant on the person eye sight on where the actual bottom of the ball is in relation to the the floor.  The angle of the wooden plank might also cause skewed values due to the calibration of the smart phone elevation app.  Lastly, the theoretical expectation of d might differ from actual real world results since the calculations do not account for the ball mass as it rolls down the ramp.  The ball can travel farther down the ramp than originally calculated.