statistical paper (1).docx

8/10/2019 Statistical Paper (1).docx

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A Study of Determining Acceleration Due to Gravity

Daniel S. Perez and Raphael C. Pascual

Mapua Institute of Technology, Mathematics Department

Probability and Statistics (Math30-5)

Abstract

Gravitational acceleration is the change in velocity on an object at a given time interval caused

by the force of gravitation. The study is conducted to determine if the carts acceleration over anassumed frictionless inclined track is equal to the component of gravitational acceleration

parallel to the inclined track and lastly, to determine if the body is dropped freely, its

acceleration is equal to the gravitational pull near the earths surface. The experiment used acart and an inclined track for the determination of acceleration due to gravity using the carts

acceleration. On the second part of the experiment a picket fence and a smart timer is used to

determine the acceleration due to gravity of a falling body.

I. Introduction

Gravitational acceleration is the

change in velocity on an object at

a given time interval caused by

the force of gravitation. The

study is related with kinematics.

According to Mapua Institute of

Technology physics laboratory

manual, Kinematics is a branch

of mechanics that consists of the

study of motion without

considering the forces that cause

or develop the motion. The

motion of the object inkinematics is represented by a

particle. In one dimensional

motion, the particle can be

considered moving along the x-

axis with a position that can be

discribed at all times.

The study is conducted to

determine if the carts

acceleration over an assumed

frictionless inclined track is equalto the component of gravitational

acceleration parallel to the

inclined track and lastly, to

determine if the body is dropped

freely, its acceleration is equal to

the gravitational pull near the

earths surface.It is said that the

motion of an object along a

levelled track is assumed

frictionless, its speed is uniform.

But if the assumed frictionless

track is inclined at an angle, its

motion is uniformly accelerated.

The acceleration of the object is

said to be equal to the component

of gravitational acceleration


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parallel to the inclined track. If a

body is dropped freely, without

air resistance, its acceleration is

said to be equal to the

gravitational pull near the earths

surface.

II. Methodology

The experiment used a cart and

an inclined track for the

determination of acceleration due

to gravity using the carts

acceleration. On the second part

of the experiment a picket fenceand a smart timer is used to

determine the acceleration due to

gravity of a falling body. Here

are the materials used and its

procedures:

Materials:

1pc Dynamics Cart

1pc Dynamics track w/ Angle

Indicator and End Stop2pc Photogate

2pc Photogate Mounting Bracket

1pc Smart Timer

1pc Smart timer Picket Fence

1pc Stand

1pc Meter stick

Procedures

PartA: Determining Acceleration

Due to Gravity Using Carts

Acceleration.

1. Set-up the track with the 0cm

end elevated using a stand as

shown in the figure, with the

end stop at the lower end and

record it as final position. See

figure 1for set-up.

2. Adjust the height of the track

to 15cm as initial height.

3. Position photogate 1 at 80 cm

and set the mode of the timer

to measure ACCEL, ONE

GATE.

4. Press button 3 of the timer to

reset.

5. Compute for the tracks

inclination using the total

length of track and its height.6. Place the cart with the picket

fence on it at the 18cm point

of the track and record its

initial position.

7. Release the cart from rest,

take the reading on the timer

and record it as acceleration.

8. Repeat steps 4 to 7 and

perform 5 trials, each trial

increasing the height of thetrack by 5cm.

9. Compute the carts total

displacement.

PartB: Determining Acceleration

Due to Gravity Using Picket Fence

and Smart Timer.

1. Set the photogate horizontally.

See figure 2 for set-up.2. With one photogate connected to

the timer, set the mode of the

timer to ACCEL, ONE GATE.

3. Press button 3 of the timer to

restart.


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4. Drop the picket fence vertically

within the photogate. See to it

that the picket fence will pass

through the photobeam

perpendicularly.

5.

Take the reading on the timer and

record it as acceleration.

6. Repeat Steps 3 to 5 and perform

5 trials.

III. Results and Discussion

For the first part of this

experiment the carts

acceleration is used to determine

the acceleration due to gravity.

Results are determined upon

performing the procedures set for

part A. Results are shown in

Table 1.

Table1: Determination of

Acceleration Due to Gravity

Using Carts Acceleration.

Trial Height

of

Track

Acceleration Inclination

()Gravitational

Acceleration

1 15 115.8 0.125 926.40

2 20 153.1 0.167 916.77

3 25 228.3 0.208 1097.60

4 30 233.6 0.250 934.40

5 35 261.1 0.292 894.18

Height is measured in cm.

Acceleration and Gravitational

acceleration in .

The results shows that as the

height of the track increases the

carts acceleration also increases.

But the gravitational force

increases on a certain point and

then it decreases. This happens

may be because of some forces

that acts on the cart and the track

that we did not include in the

experiment such as friction, since

we only assume that the track is

frictionless.

Hypothesis:

at

Area of rejection is .

Since the value of t is equal to -0.715 and it

does not fall under the rejection region, we

are to accept the null hypothesis and reject the alternative.


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On the second part of thise experiment

which is to determine the acceleration due to

gravity of a body dropped freely, we follow

the procedures set on PartB. The reults are

recorded and are shown in Table 2.

Table2: Determination of Acceleration Due

to Gravity Using Picket Fence and Smart

Timer.

Trial Acceleration

1 982.6

2 975.2

3 981.34 971.3

5 971.8

Accelerations are in . Ressults shownare very close to our claim that the

acceleration of a body dropped freely is

equal to the gravitational pull near the

earths surface, .

Hypothesis:

at

Two tailed test.

is our rejectionarea. But the value of t computed is -1.51

and it is greater than -2.776.

Since the value of t does not fall in our

rejection region which is , we are to accept the null hypothesis and reject thealternative.

IV. Conclusion

With the help of the materials, it is

observed in table 1 that as the height

increase the acceleration of the cart or anyobject also increase. However according to

the date we can conclude that thegravitational acceleration has a different

relationship with the height and the

inclination of the track since its results isdifferent from the acceleration of the cart.As for the hypothesis the null hypothesis is

accepted because is greater than the thevalue of the area of rejection. The second

part also provided a conclusion which

claims that a body subject to a free fallmotion has an acceleration equal inmagnitude to the gravitational pull near the

earths surface.It accepts the null hypothesis

and rejects the alternative because its didnot fall under the area of rejected region.


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Appendix

Figure 1: Set-up for Determination of

Acceleration Due to Gravity Using Carts

Acceleration.

Courtesy of: honorsphysicsrock.wikispace.com

Figure 2: Set-up for Determination of

Acceleration Due to Gravity Using Picket

Fence and Smart Timer.

Courtesy of:www.vernier.com

Reference:

[1] Mapua Institute of Technology Physics

Laboratory Manual
http://www.vernier.com/http://www.vernier.com/

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