9- Sept- 2014 Projectile motion

Projectile Motion Lab

Objective: 

 To use what we know from projectile motion to predict the impact point of a ball on an inclined board.

Set- up:

 We used a simple apparatus that involved aluminum tracks (one at an incline and the other at a horizontal on top of a table/ desk) seen in (fig 1), a wooden plank longer than the height from the floor to the top of the rail, a steel ball, carbon paper attached to a regular sheet of paper that's taped to the ground where it is estimated for the ball to hit. From there you will need an angle finder for the plank, and a 2 meter stick to do other necessary measurements like the height from the end of the track relative to the ground.

Figure 1. the aluminum tracks assembled
to roll the ball off the table and onto the floor
or the inclined surface

Part I:

During the first part of the experiment, you need to have you apparatus set up and the papers on the relative area where the ball will impact the ground. After getting 5 consistent tries and your point of ball release is marked on your railing, you must get the 2 meter stick and measure your mark from the carbon paper from the base of the end of the track as well as its height relative to the ground, see in (fig 2). From there, you are asked to calculate you vo :

y= 1/2* (g)* t^2

Since our y= .942m,

(.942)= .5* (-9.81) * (t^2)

t= .483s

Now, it is assumed that the acceleration for x is zero and our initial velocity in the y direction is zero as well, with our given time we find our initial velocity to be:

vo=  (x)     

(.483s)

We found our x =.663± .002 m because we were confident in our time and y measurement, but the place where the ramp ended was a small yet noticeably off from the edge of the table where we used as reference for the measurement, in this case:

vo= (.663m) = 1.514 ± .006 m/s

(.483s)                      

Part 2:

 Our next step was to predict that if we put an inclined plank from the edge of the ramp to the floor at an angle (alpha) where would the ball land. Assuming that the apparatus was not altered in any way, the initial velocity will still be the same. Below in (fig 2.) Are diagrams and work showing the the derivation of the equations for each part of the lab.

Figure 2. The derivation of each part of the
 lab and final calculations for the vo and distance d on the inclined surface 

The equation from above that we were able to derive for our angle (alpha) and vo would be:

alpha = .8378± .0175 rads

vo = 1.514 ± .006 m/s

d= 2* tan(alpha)* (vo)^2 = 2* (1.1106) *(1.514^2) = .776 ± .022m

      g                                    (9.81)                        

We've also included our uncertainties that we found in the figure below.

Figure 3. Derivations of both equations used in this lab and their uncertainties.

If we compare the experimental results with the theoretical results:

Theoretical: .774 ± .022 m

3% uncertainty

Experimental: .794 m

+2% more than theoretical

Sources for uncertainty lie in mostly in the rotational friction from the track that was not put in account. Error may have been from an inconsistent placement of the steel ball when beginning a trial, and small measurement errors.