Faculty Of Engineering And Information Technology

MEE 3219 Engineering Dynamics

Lab Report

Experiment 4:

Acceleration due to Gravity

Name : Ehsan Samoh

Program : BMEGI

ID : I14005275

Date of experiment conducted : 10th of Feb 2015

Date of submission: 24th of Feb 2015

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Table of Contents

4.1 Objectives 3

4.2 Theoretical Introduction 3

4.3 Equipment and Procedure3

4.3.1 Equipment 3

4.3.2 Procedure 3

4.4 Results and discussion 4

4.6 Conclusion 6

4.7 Reference 6

List of Figures

Figure 1: The set up of the experimental equipment 3

Figure 2: Bar graph of time taken from A to B (s) 4

Figure 3: Bar graph of acceleration through light gate A and light gate B (m/s2) 5

Figure 4: Graph of Force (M+m)a against mass (m) 5

List of Tables

Table 4.4.1: Data of velocity, time and acceleration due to gravity 4

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4.1 Objective

To determine the ‘g’ the acceleration due to graity.

4.2 Theoretical Introduction

Acceleration is defined as the rate at which the velocity of a moving object changes with time. Accelerations are always caused by forces. In this laboratory we will investigate the acceleration due to the force of gravity.

In its simplest form, Newton's law of force relates the amount of force on an object to its mass and acceleration.

F = m a

or force = mass times acceleration. Therefore, to impart an acceleration to an object, one must impart a force.

This result was first demonstrated by Galileo when he dropped cannonballs of different masses (weights) from the Leaning Tower of Pisa to show that although they had different masses, when dropped together, they landed together. This happened in this manner because they both experienced the same acceleration. A similar experiment may also be performed by dropping a coin and a feather. When dropped in air, the coin always lands first, but when they are dropped in a vacuum, an environment where there is no air, they land together! In the coin and feather case, the different velocities are due to another force called air friction.

4.3 Equipment and procedure

Equipment : The equipment consist of a vehicle, a blower unit, a blower unit, Velcro weights for adding to the vehicle, a computer to record the data for further investigation a pulley cord, a weights set for the pulley cord and to light gates for measuring the speed of the vehicle as show in the picture below in figure 1.

Figure 1: The set up of the experimental equipment

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4.3.1 The equipment is set as illustrated in the picture above4.3.2 The light gate is set to a positions so that the vehicle passes through both

detector before the pulling mass hits the floor.4.3.3 Place a total mass of 20g on the end of the cord holding the trolley.4.3.4 Switch on the Air apply.4.3.5 Release the trolley and record the velocity at light gate A and light gate B as

well as the time in between.4.3.6 Repeat step 2.5 twice to ensure consistent results.4.3.7 Repeat for increments of 20 g up to a maximum of 100 g.4.3.8 Plot a graph of ( M + m ) a versus m, the gradient of which should give the

value of ‘g’

4.4 Data and discussion

ReadingSpeed at A

Speed at B

Time from A to B

Mas, m Mass, m Acceleration, a

(M+m) a

m/s m/s s g Kg m/s1 0.29 0.69 0.40 20 0.02 0.24 0.05282 0.35 0.83 0.48 30 0.03 0.69 0.15873 0.39 0.94 0.55 40 0.04 0.89 0.21364 0.45 1.04 0.59 50 0.05 1.08 0.2705 0.42 1.09 0.67 60 0.06 1.22 0.31726 0.46 1.16 0.70 70 0.07 1.35 0.36457 0.48 1.21 0.73 80 0.08 1.47 0.41168 0.54 1.25 0.71 90 0.09 1.56 0.45249 0.56 1.25 0.75 100 0.1 1.68 0.504

Table 4.4.1

The result obtain from the experiment is plotted in table 4.4.1

Figure 2

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The red bar and blue bar in figure 2 represent the time taken for the vehicle to passes gate A and gate B by the computer following an increase in mass of trolley at the end of the cord.

Figure 3

The bars in figure 3 represent the acceleration generated by the computer when the vehicle from point A to B following an increase in mass of the trolley.

A graph of mass versus (M + m) a is obtained based on the results

10 20 30 40 50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

0.0528

0.1587

0.2136

0.270.3172

0.36450.4116

0.4524

0.504

graph of mass vs (M + m) a

mass of trolley (g)

(M +

m) a

Figure 4

It is found that the mass of trolley is directly proportional to (M + m) a which is approximately equal to the Newton 2nd law (Wikipedia).

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It is found that the mass of the trolley is directly proportional to (M + m) a as stated in figure 3.4 . The value of gravitational acceleration is know as a constant SI unit which is 9.81m/s². The theory is proved by another researcher. The gravity of Earth, which is denoted by g, refers to the acceleration that the Earth imparts to objects on or near its surface. In SI units this acceleration in newton per kilogram. It has an approximate value of an object falling freely near the earth surface will increase by about 9.81 meters per second every second. There is a direct relationship between gravitational acceleration and the downwards weight force experienced by objects on earth, given by the equation F=ma (force = mass x acceleration) (Engineering Mechanic Dynamics, 2005).

4.5 Conclusion

The experiment conducted was successful as it helped establish a relationship between the mass and (M + m) a. The acceleration of gravity measured in this lab verified that the accepted value of g is 9.81 m/s² to within the uncertainty of the experiment.

4.6 Reference

4.6.1 Southern Methodist University available online at http://www.physics.smu.edu/~ryszard/1313fa97/1313-Acceler_.PDF

4.6.2 Engineering Mechanic Dynamics SI EDITION, 2005

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