# Motion Down an Incline

Shaoren Yuan

October 5, 2013

Physics 1301W, professor: Dr. Zudov, TA: David

Abstract

The processes of a cart rolling up and returning back along a track were recorded, and the processes (motion of the cart.) were described as equations. Also, we calculated the accelerations of every stage (aup, adown and ahighest). Then the relationship among aup, adown and ahighest was concluded. Finally, the acceleration was measured and was proved from data.

Introduction

If there is a car launched from the bottom of an incline and it goes up until reaching the highest point, then it reverses its direction. To ensure the safety under this circumstance, the accelerations of every stage need to be

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Finally, the acceleration of every trial was known, which equaled to the slope of line in every graph. Then we repeated the procedures for four times and got the data and the graphs of the four parallel tests.

Data

The followings are the V-t graphs of these four trials.

The thickness of two blocks, H, was 19.30cm and the length of the track, L, was 226.10cm. Thus the theoretical value of the acceleration was: g*sinθ=0.8365m/s2.

Analysis

The equation in every graph was written as this form: V=C-k*t (the letter “y” here means the velocity, v; and “x” here means time, t). The letter –k, which was the slope of the line in the graph, will be explained in the later part. Then, the letter C in the graph means the initial velocity because when t=0, then V=V(0)=C-k*0=C. Moreover, the initial velocity was respectively: 0.4746m/s, 0.4693m/s, 0.4861m/s, and 0.501m/s. The average initial velocity was 0.4828m/s.

It is noticed that the goodness of fit (R2) in the four graphs are bigger than 0.8, which means that the data was reliable and these points were well selected. Moreover, it also explained that in one graph, whether the points were above the X-axis or not, all of them could be considered at the same line. Thus the slope of the graph was a constant, which meant that the acceleration did not change during the motion process. Therefore, it is proved that aup=adown=ahighest mentioned in