1.0 Introduction

Earth’s gravity will pulls all the objects to the earth’s surface. When the gravity force is the only force that acting on the object, the object will undergo free fall. An object that in state of free fall will experience a downward acceleration of 9.81 m /s2.

2.0 Theory

All masses have gravitational attraction toword another. A body on earth has a value of gravitational attraction that keeps the body on the ground. When this body is lifted, it carries an energy known as the potential energy P, which is calculated, based on the mass of the body m, gravitational acceleration g and height h as shown below:

P=mgh

When the body is release, gravitational force acts in forcing the body to fall to the ground and potential energy is convert into kinetic energy V, whichis calculated based on the mass of the body m and the value of speed of its fall v as shown below:

V=12

mv2

Thus, gravitational attractions plays an important role in determining the response of a body when experiencing free fall. When a body fall to the ground from a certain height h, it falls at gravitational acceleration. The gravitational acceleration of earth is measured based on gravitational constant, G, masses of bodies m1, m2 and the distance between bodies r2 as shown below:

g=G m1 m2/r2

Since the mass of the earth is far larger than any body on earth, the value of mass pf body on earth is neglected. By taking the value of G = 6.6742 x 10−11 m3 kg−1 s−2, mass of earth

m1=5.98 ×1024kg and the radius of earth r (6.378 x 106 m), a standard value for gravitational

acceleration is derived as 9.81 m /s2.

The forked light barrier measure the free fall phenomena by measuring the time t when the body, a steel ball in this case, enters the light barrier and exits the light barrier. Thus, by knowing the diameter of the steel ball d, instantaneous velocity v is calculated using the equation below:

v=d /∆ t

3.0 Procedure

Figure 1: Set-up of apparatus Figure 2: Example experiment

1. Setup the free fall apparatus as shown in the Figure 1.2. For the distance of fall of 90 cm, shift the forked light barrier downwards by 90 cm.3. Unscrew the knurled screw of the holding magnet, put the cord through the hole and

suspend a weight from it.4. Adjust the arrangement so that the cord interrupts the light barrier.5. Remove the cord and screw the knurled screw in again.6. Placed the steal ball to the magnet, and screw the knurled screw back until the steel ball

just hanging underneath the magnet.7. Suspend the steel ball, and start the measurement with the key start/stop.8. As soon as the ball has fallen down (shown in Figure 2), press the key start/stop once

more.9. Read the time of fall t as displayed in the digital counter.10. Press the key ∆ t two times, record the obscuration time ∆ t in ms.11. Repeat the step 2 until 10 for differences as stated in the given table.

4.0 Experimental Data

Table 1 : Time of fall and obscuration time for different distance

Distance of fall, h (m)

Time of fall, t (s ) Obscuration time, ∆ t (ms)T1 T2 T3 average ∆T1 ∆T2 ∆T3 average

0.1 0.182 0.183 0 .181 0.182 7 .339 8 .213 10 . 688 8.747

0.2 0.238 0.238 0 .238 0.238 6 .596 8 .758 8 .966 8.1130.3 0.277 0.274 0.274 0.275 7 .565 7 .358 7 .192 7.3720.4 0.312 0.313 0.311 0.312 6 .196 4 .462 4 .625 5.0940.5 0.344 0.344 0.344 0.344 6 .035 6 .063 6 .019 6.0390.6 0.374 0.373 0.374 0.374 4 . 977 5 .029 5 .037 5.0140.7 0.401 0.401 0.402 0.401 4 .312 4 .303 3 .445 4.0200.8 0.428 0.429 0.427 0.428 3 .471 3 .249 2 .072 2.9310.9 0.451 0.452 0.453 0.452 3 .698 4 .506 3 .502 3.902

5.0 Experimental Result

Table 2 : Calculated values for instantaneous velocity and time of fall squared

Distance of fall, h (m)

Average of time of fall, t (s)

Average of obscuration time, ∆t (s)

Instantaneous velocity, v

(m/s)

Time of fall

squared, t 2(s2)

0.9 0.452 3.902 0.00487 0.2040.8 0.428 2.931 0.00648 0.1830.7 0.401 4.020 0.00473 0.1610.6 0.374 5.014 0.00379 0.1400.5 0.344 6.039 0.00315 0.1180.4 0.312 5.094 0.00373 0.0970.3 0.275 7.372 0.00258 0.0760.2 0.238 8.113 0.00234 0.0570.1 0.182 8.747 0.00217 0.033

6.0 Discussion

0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Graph 1: height(m) againt time(s)

time(s)

he

igh

t(m

)

6.1 From the first graph of height (h) against time (t) graph, we found that the curve line crossed most of the points in the graph about 5 points of 9 points. When the average time of fall is 0.452 seconds, the distance of fall is 0.9m. As the average time of fall decreased until 0.182 seconds, the distance of fall keep on decreasing until 0.1m. The relationship between those 2 variables is the lower the average time of fall, t (s), the lower the distance of fall. The distance of fall increase linearly with average time of fall, t (s). As the load is higher from the ground, the potential energy increases too which uses the formula P=mgh.

Example 6.1.1

P=mgh

= (mass) (9.81m/s )(0.1m)∗

Example 6.1.1

V = 1/2 mv∗

= ½ (mass) (0.9 m /0.452 s )

Slope = (0.8−0.4 )m

(0.0973−0.1832)t 2 = 4.65 m

t 2

6.2 In graph 2, we have drawn height (m) against the time squared, t (s ). We obtain a∗ ∗ curve with the gradient of the slope increasing. When the Time of fall squared, t (s ) is∗ ∗ 0.204s , the height is 0.9m. As the time of fall squared, t (s ) decreased to 0.033s , the∗ ∗ ∗ ∗ height also reduced to 0.1m.This curve has 4 points crossed out of 9 points for the best fit curve. The relationship between those variables is as the Time of fall squared, t (s ) decreased, the∗ ∗ gradient of the curve also decreased. This curve intersects the y-axis at 0.076m. Relating to the theory, when the Distance of fall or height which the unit is metre (m) divided by Time of fall squared, t which the unit seconds squared (s ), we will obtain ms*-2 or the acceleration of the∗ ∗ metal ball.

Example 6.2.1

G = (G)(m1)(m2) / (r*)

= (6.6742x10*-11)( m*3)(kg*-1)(s*-2) x (5.98x10*24 kg) x (m*2) / (6.378x10*6m)

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.220

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Graph 2: Height(m) against Time square(t^2)

Time square(t^2)

He

igh

t(m

)

0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Graph 3: velocity(m/s^-1) against time(s)

time(s)

velo

city

, m/s

^-1

Slope = (0.0047−0.0022 )m / s−1

(0.401−0.182)s = 0.01142 m

6.3 The 3rd graph is velocity of the metal ball (m/s) against the time (s) of the free fall. From the best-fit curve graph drawn by us, we found that the velocity (m/s) is also not directly proportional to the time (s). It increases linearly and intersects the y-axis at 0.00151 m/s.

There are 3 differences between the 2nd graph and the 3rd graph. First, 2nd graph intersects the y-axis at 0.076 m while the 3rd graph intersects the y-axis at 0.00151 m/s. Second, as the time-squared increases in graph 2, the gradient of the slope increased. The gradient in graph 2 is 5. While in the 3rd graph, as the time (s) increases, the gradient of the slope decreased. Third difference that we have observed is in the 2nd graph, the curve passed through 5 out of 9 points of the graph while in 3rd graph, the curve only passed 4 out of 9 points to obtain the best fit-curve.

Example 6.3.1

G = (G)(m1)(m2) / (r*)

= (6.6742x10*-11)( m*3)(kg*-1)(s*-2) x (5.98x10*24 kg) x (m*2) / (6.378x10*6m)

6.4 There are about 3 errors that we have found out during we did our experiment. First is the common parallax error. We found out that it is difficult for our eyes to be perpendicular to the reading of the metre rule because the 1 metre ruler is on top of the table. We have to stand on the chair and the ruler and the holding magnet clamp must near to each other. Second error is systematic error. The type of systematic that we faced is the instrument is not firm and stable. The screw is not tight so the whole instrument and the holding magnet with clamp also shook. Therefore, we find it difficult to adjust so that the metal ball dropped passing the forked light barrier. Third error is random error. There are few times our friends calculated wrongly or wrote the data or result incorrectly. Luckily, we can detect because the difference between those values are obvious. Example, during our second reading for height 0.2m , our friend wrote 8.996 s instead of 8.113 s wrongly because the table is confusing. Finally, the theoretical value is for sure higher than the experimental result. It is because of time increase. In this case, air friction between the metal ball and the air and wind direction also can affect slightly the result of our experiment. The average difference of time recorded is about 0.003 sec only.

7.0 Conclusion

From the experiment we did, we have understand free fall better and the concept of it. I learned that when an object falls under the influence of gravity, its velocity increases at a constant speed and the average of this speed is about g = 9.8. Even though there are about 4 errors that we faced while doing this experiment, it is still good considering the equipment we have is kind of old. We also learned advanced techniques of building tables, writing equations, and putting Greek symbols using the Microsoft Excel. Overall, this was a great learning experience and a great cooperation with our friends.

8.0 Reference

Ferdinand P. Beer, 2010, Vector Mechanics For Engineers Statics and Dynamics, Ninth Edition, McGraw-Hill Companies, Inc, Americas, New York,

http://en.wikipedia.org/wiki/Free_fall R.C. Hibbeler, 2007, Engineering Mechanics Dynamic, 11th Edition SI Units, Pearson

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