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Paul Sanders
Phys 141 Sect. 16
Range Vs. Height Lab
Goals:
The goal of this experiment is to perform several experiments in order to determine the
function for the range, R, of an object in terms of the height that the ball is dropped from, H, and
the height at which it hits a bounce plate, h. We will use the data gained to determine the
empirical relationship and coefficient of restitution between height and range.
Theory:
In this experiment we needed to determine a function for R using H and h, and began
with the equations R=vt and H=H
0
+ V
0
t + 1/2gt
2
.
We will start with the second equation.
Since
the initial height (H
0
) and velocity (V
0
) are zero, we can rewrite the equation as H=1/2gt
2
.
We
then solve the equation for t and get t=
2Hg
.
When we plug that into the R=vt equation we get
R=v*√(2H/g).
To find R, however, we still have to find v, so we use the equation V=V
0
+ gt.
Once again we cancel out V
0
and substitute √(2H/g) for t.
This gives us V=g
,
2Hg
which gives
us V=
.
2gH
We now return to the equation R=vt, and make the necessary substitutions to get
R=
2gH
*
2hg
.
We simplify this to get
*
,
4h H
which is our final equation.
Procedure:
This experiment was divided into three major parts.
In part 1, the object was to observe
the scatter in data and how it was affected with more drops.
To do this we set both heights, H
and h, to about 20 cm, placed a piece of carbon paper over a large piece of regular paper, and
dropped the ball through the drop plate, reflecting it off the bounce plate and recording where it
marked the paper.
Before dropping the ball, we defined the origin point by dropping the ball
through the drop plate and not reflecting it off the bounce plate.
We then dropped the ball
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 Spring '08
 Dienes

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