# Arithmetic Mean and Bounce Plate

**Topics:**Arithmetic mean, Statistical dispersion, Statistics

**Pages:**5 (1086 words)

**Published:**February 21, 2011

Abstract

The goal behind this experiment was to estimate the distance a ball would travel after it falls a certain distance and bounces off a metal plate which has an angle of 45 degrees. To find this we had to take the basic equations for kinematics which are (1/2)at2=x and v=v0+at and combine them to make an equation that will help us solve for the distance the ball will travel after hitting the bounce plate. The equation came out to be R=g*(sqrt(2)/sqrt(g))*(sqrt(H)*sqrt(h)), as that g is acceleration of gravity, h is the height of bounce plate, and H is the height of where the ball will be dropped. After completing this experiment the result was that the standard deviation was +/- 2.3 cmfrom the average value of 26.5cm. This was used for each variable H was 20cm and h was 20cm. Also there 18 trials performed as well.

Introduction

This experiment was to use kinetics of projectile motion and free falling bodies to determine the distance a ball will travel after it hits a bounce plate. To determine this we had to use the equations x=(1/2)at2 and v=v0+at and derive an equation that will determine the distance the ball will travel based on the height of the bounce plate and the height of where the ball will be dropped above the bounce plate. The equation made was g*(sqrt(2)/sqrt(g))*(sqrt(H)*sqrt(h)). From here we can make an estimate of how far the ball will travel after it hits the bounce plate.

Procedure

Materials needed:

• Steel Ball

• Bounce Plate 45 with a 45 degree angle

• A platform to drop the ball from

• A post to attach the bounce plate and platform to

• Carbon Paper

• Paper

• Meter Stick

[pic]

fig- shows the experiment setup

The first part of this procedure is to observe the scatter in the data, how the estimate of the range,R, for a fixed height varies with additional drops, and how the estimate in the uncertainty in the range varies with additional drops. The second part is that for a fixed height, try several different methods of dropping the ball. Compare the average and spread (error bars) of the range for the different methods.

To perform this experiment one must set up the post with the drop platform and bounce plate attached to it. Make sure you measure the bounce plate and drop platform to the appropriate chosen heights used in the equation. Make sure you have a large piece of paper taped to the table with a piece of carbon paper placed over it. Then drop the ball through the platform as many times as desired. Take measurements and find the average distance and the standard deviation and compare to estimated distance. The imperfections in the bounce plate and variations in the release of the ball will cause scatter in the data. A ball released twice from the same height will not hit the paper at the same place

Height (H) variable-

H=1/2g t^2 [ t= sqrt 2H/g) [ calculating the height using gravity and time)

V(1)= gt(1)---V(1)=SQRT2Hg(calculate velocity using gravity and height)

Height(h) constant

V(2)----sqrt2h/g ( calculating velocity using height and gravity

X=V(2)*t(2) calculating position

Data

| |TRIAL 1 |TRIAL 2 |TRIAL 3 |TRIAL 4 | |h(cm) | 20 |20 |20 |20 | |H(cm) | 10.5 |20 |15 |5 | | sqrt (H) | 3.2 |4.5 |3.9 |2.2 | |X(1) |17.4 |24.5 |24.7 |14.3 | |X(2) |20.3...

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