Lab 6: Physics 4A Trajectories

                                                            Trajectories Laboratory 
                                                                 I-Shou Lin  & Kirk Paderes
                                                                        March  15th, 2017'
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Explore the behavior of projectile motion in two dimension in order to determine the impact point of a ball on an inclined board.

When a projectile is in motion across space, the horizontal and vertical components of its motion may seem related and indistinguishable. However, the horizontal and vertical components of its velocity are independent of each other, and the only quantity relating them is time. When a projectile motion is in free fall, only its vertical motion is affected by the acceleration due to gravity. Its horizontal component of velocity remains constant. The horizontal and vertical components of its velocity can be combined together through vector addition to yield the overall velocity at a given point in time.


The laboratory procedure consisted mainly of setting up the apparatus                    
                            
The black cover at the floor is carbon paper that leaves a mark when the ball lands on it. The ball starts accelerating and falls on the floor on top of the carbon paper. From the measurements, determine the ball's horizontal velocity. Then, attach a board such that it couches the end of the lab table and the floor. Place carbon paper to determine where the ball lands on the paper which is on the board. 

                                             Data Table
                 

Horizontal distance	Height	Distance	Angle
67.3+/- 0.1 cm	89.1 +/- 0.1 cm	70 +/- 2 cm	46 +/- 0.5

     

                                                           Calculated Results

                         velocity= ( 1.578 m/s to 1.579 m/s to 1.581 m/s) 

Distance= ( 0.737 m to 0.758 m to 0.780 m)


Conclusions 

This trajectory laboratory was really simple and straightforward. Assembling the apparatus was self-explanatory and easy. For the first part of the lab where the horizontal velocity needs to be determined from the height and displacement, measuring the height is easy, but for the displacement, it's where the uncertainty values come to play with the impact points of the steel ball on the carbon paper. Since the steel ball is dense, has a small surface area, and drops from a low height, the air resistance's effect on the ball is negligible. The second part of the lab was more interesting because now there was a board that was elevated at an angle to the ground in which the ball would have to strike. The derivation of the formula for the distance is in the photo. Then we performed the experiment and compared the theoretical to the experimental results for distance.  The propagated uncertainty for the distance was 0.22 m due to the uncertainty in the displacement and subsequently the velocity of the ball. Differences between the experimental and theoretical values for distance is 5.8 cm a intermediate range, 5.7 cm for lower bound. and 6 cm for the upper bound. These significant differences is likely the result of propagated uncertainty values from measurements and setup of apparatus that affected later results.