PHYS111

Formal Report 2

University of Canterbury

Campbell Moulder

Abstract

The force of gravity is said to be a constant of 9.81 ms-2 (3). This can be proved by measuring the projectile motion of a bouncy ball and plotting a ∆Vertical Velocity vs. Time graph, the gradient of which should equal the constant force (acceleration due to) of gravity. Our gradient value of 10.26±0.49 ms-2 is consistent with the actual value of 9.81 ms-2. Introduction

A projectile is an object that has been launched into the air. Once a projectile has been launched, the only forces acting are: Air friction (this is considered negligible in our experiment) Lift force, if the object is behaving like a wing (this is also negligible as our object is a ball) Gravity, the weight force which acts downwards (this is the value we will be calculating in our experiment) In our experiment we will measure the projectile motion of a bouncy ball using the computer programme Motion Tracker. The results of this experiment will allow us to plot a ∆Vertical Velocity vs. Time graph. The only force that is affecting the ball that we are taking into account is the force due to gravity; therefore the gradient of this graph will give us the value of the force or acceleration due to gravity. The horizontal component is negligible because once the ball has left our hand the only force acting is downward, the horizontal force remains constant. The objective of our lab experiment is to either confirm or deny the hypothesis that the value of gravity is a constant and is equal to 9.8ms-2. Materials and Methods

1Computer with webcam and projectile motion analysis program installed 1Lightweight Bouncy Ball

1Carpenters Square with wooden support

1Metre Ruler

1Clamp Stand

We set up the apparatus according to the PHYS111 lab manual: We stood the Carpenters Square up on the bench and attached the camera to the clamp stand at a height so the Carpenters Square ran parallel with the x and y axis of the camera. We then bounced the ball through the path of the camera and recorded its motion. This proved to be difficult at times because the ball had to travel along the x-axis of our carpenters square in order for us to get an accurate example of projectile motion. Also the ball had to bounce within the boundaries of the camera so that the full motion of the ball could be recorded. Using the motion tracker program we then marked out centre of the ball frame by frame as it travelled across the screen. We took the x and y values of the plotted points and this gave us our projectile motion graph. We then plotted a Velocity VS Time graph and took the gradient; this gave us our value of gravity. Results and Analysis (1)

Table 1 Time (s) x and y axis (cm) results from Motion Tracker programme t (s)| x (cm)| y (cm)|

0| 0| 6.1|

0.031| 3.4| 11.5|

0.063| 7| 15.9|

0.094| 10.5| 19.6|

0.125| 14.4| 22.7|

0.156| 18.2| 24.7|

0.203| 22| 25.5|

0.25| 25.8| 25.2|

0.281| 29.9| 24|

0.313| 34| 21.4|

0.344| 38.1| 17.6|

0.375| 42.2| 12.4|

0.406| 46.1| 6.1|

Figure 1 The Projectile Motion of a bounce ball

We then manipulated the data from Table 1 to calculate ∆t (s), ∆y (cm), Vy (cm/s) and Vy (m/s).

To calculate ∆t we took the difference between two consecutive time values e.g. 0.32-0.31=0.31, therefore the change in time for the given two will be 0.031s. To calculate the ∆y we used the same process as for the ∆t. We then needed to calculate the Velocity of the ball in the y direction. To calculate the velocity of an object the formula v=d/t can be used. From the results of our experiment we knew the distance the ball travels and the time it takes. This allowed us to calculate the vertical velocity of the ball.

Table 2 ∆t, ∆y and the velocity of the ball in the vertical direction ∆t (s)| ∆y (cm)| Vy (cm/s)| Vy (m/s)|

0| 0| 0| 0|

0.031| 5.4| 174.2| 1.742|

0.032| 4.4|...