blog 5

Projectile motion lab 

In this lab, we attempted predict the impact point of a ball rolling off of a ramp onto an inclined plane using our knowledge of projectile motion.

The ramp was set at a fixed angle, and the length of the ramp was predetermined by measurement. The ramp and ball were both made of metal, and so it was assumed that friction was negligible, and for the sake of simplicity, the ball was modeled as a sliding object rather than a rolling one, so that rotational forces and slipping could be ignored. The setup is pictured below:

In order to determine the initial velocity of the ball at the end of the ramp, we first did several trials allowing the ball to fall onto the floor unobstructed. In order to measure its velocity, we assumed that it was moving perfectly horizontally when it left the ramp. That is that Vy0=0. We also measured the distance from the top of the ramp to the floor, giving us a value for the displacement on the y axis. We then put a piece of graphite paper on the floor above a piece of white paper that was taped down. We allowed the ball to roll of the ramp and strike this piece of paper 5 times, each time leaving a mark on the white paper. We then measured the distance from the bottom of the ramp (superimposed on the floor) to that point. Now, having an x and y displancement, a a value for vy0 and acceleration, we are able to use kinematics equations to find intial velocity of the ball as it exits the ramp as follows:

y=1/2at^2                            x=vt

0.942=1/2(9.8)t^2               0,663=v(0.483)

t=0.483 s                              v=1.514 m/s

We then set up an inclined board underneath the ramp, as shown in the diagram below:

Our task now was to figure out distance d that the ball would travel before striking the ramp. We could determin alpha and of course we had just obtained initial velocity. The equation was derived as follows:

We then ran the ball through the ramp and measured where it struck the board, which ended up yielding a value d=0.794m, which is roughly 2.3% above our expected value. This discrepancy is most likely due to some measurement error or the fact that we approximated our model assuming no friction or rolling.