UNIVERSITI TEKNOLOGI MARAFAKULTI KEJURUTERAAN KIMIA

ENGENEERING PHYSICS LABORATORY (CHE 175)

NAME : SITI NOR SAMRAH A.RAHIM NOOR SYAFIQAH AMERAH BT AHMAD TARMIZI ABDUL HALIM BIN NORDIN NURUL ADILAH BT NASARUDDIN MUHAMMAD RAZI BIN ZAHARISTUDENT NO. :2008291992 2008293072 2008293172 2008292022 2008424824GROUP :2EXPERIMENT : CENTRIPETAL FORCEDATE PERFORMED : 21 JANUARY 2009SEMESTER : DISEMBER 2008 – APRIL 2009PROGRAMME/ CODE : DIPLOMA IN CHEMICAL ENGINEERING / EH110

No Title Allocated marks (%) Marks (%)1 Abstract/Summary 52 Introduction 53 Aims / Objectives 54 Theory 55 Procedures 36 Apparatus 57 Results 208 Calculations 109 Discussions 2010 Conclusions 1011 Recommendations 512 References 513 Appendices 2

Total 100 Remarks:

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TABLE OF CONTENTS

Abstract 3

Introduction 4

Objectives 5

Theory 5

Procedures 6

Apparatus & Chemicals 9

Results 10

Calculations 12

Discussions 15

Conclusions 16

Recommendations 16

References 17

Appendices 18

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ABSTARCT / SUMMARY

The objective in this experiment is to study the effects of varying the mass of the

object, the radius of the circle, and the centripetal force on an object rotating in a circular

path. For the first experiment of vary radius with constant force and mass, the larger the

radius, the period (T) is increase. Meanwhile, for the second experiment of the vary force

with constant radius and mass, the larger the force, the shorter the period of time to

complete four revolutions. Lastly for the third experiment of the vary mass with constant

radius and force, when the mass of object increased, the larger the centripetal force.

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INTRODUCTION

According to Newton’s second law (net force = ma), an object that is accelerating

must have a net force acting on it. An object moving in a circle, such as a ball on the end

of a string, must therefore have a force applied to it to keep it moving in a circle. That is,

a net force is necessary to give it centripetal acceleration. The direction of the net force is

continually changed so it is always directed toward the center of the circle. This is

sometimes called a centripetal (“pointing toward the center”) force.

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OBJECTIVE

The objective of this experiment is to study the effects of varying the mass of the

object, the radius of the circle, and the centripetal force on an object rotating in a circular

path.

Centripetal force

a. Understand that uniform circular motion is due to the action of the resultant that is

always directed to the circle

b. how to use the formula ν = rω, ω = 2π

T

THEORY

In this experiment, when an object of mass, m, attached to a string of length r, is

rotated in a horizontal circle, the centripetal force on the mass is given by:

F = mv² = mrω²

r

where v is the tangential velocity and ω is the angular speed (v = rω). To measure the

velocity, the time for one rotation (the period, T) is measure. Then:

v = 2 п r

T

And the centripetal force is given by:

F = 4п²mr

T²

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PROCEDURE

Part 1: Vary Radius (constant force and mass)

1. In this part of the experiment the centripetal force and the mass of the hanging

object will be held constant. Object will be weigh and its mass must be record in

Table 3.1.the string from the spring must be connected to the object and the object

must be hanging from the side post. The string must under the pulley on the centre

post.

2. The clamp-on pulley would be attached to the end of the track nearer to hanging

object. String attached to the hanging object and hangs a known mass over the

clamp-on pulley. Mass recorded in Table 3.1.This established the constant

centripetal force.

3. Radius by aligning the line on the side post with any desired position on the

measuring selected. Tighten the thumb screw on the side post while pressing

down on the side post to secure its position. Radius recorded in the Table 3.1

4. Hanged vertically the object on the side bracket. On the center post, the spring

bracket vertically adjusted until the spring from which the object hangs on the

side post is aligned with the vertical line on the post.

5. The indicator on the center post aligned with the orange indicator.

6. The mass that is hanging over the pulley removed and the pulley removed.

7. Apparatus rotated, the speed increased until the orange indicator centered in the

indicator bracket on the center post. This indicates that the string supporting the

hanging object is once again vertical and thus the hanging object is at the hanging

object is at the desired radius.

8. The speed maintained, stopwatch used to time four revolutions. The time by four

divided and the period recorded in the Table 3.1.

9. The side post moved to a new radius and the procedure repeated. Total of three

radii done.

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Part 2: Vary Force (Constant Radius and Mass)

The radius of rotation and the mass of the hanging object will be held constant for this

part of the experiment:

1. Object weighed and it mass recorded in Table 3.3. The object hanged from the

side post and the string from the spring connected to the object. The string must

pass under the pulley on the center post.

2. The clamp-on pulley attached to the end of the track nearer to the hanging object.

String attached to the hanging object and hangs a known mass over the clamp-on

pulley. This mass recorded in Table3.3. Centripetal force determined.

3. Radius by aligning the line on the side post with any desired position on the

measuring tape selected. Tighten the thumb screw on the side post while pressing

down on the side post to secure its position. Radius recorded in the Table 3.3.

4. Hanged vertically the object on the side bracket: On the center post, the spring

bracket vertically adjusted until the spring from which the object hangs on the

side post is aligned with the vertical line on the post.

5. The indicator bracket on the center post aligned with the orange indicator.

6. The mass that is hanging over the pulley removed and the pulley removed.

7. Apparatus rotated, the speed increased until the orange indicator centered in the

indicator bracket on the center post. This indicates that the string supporting the

hanging object is once again vertical and thus the hanging object is at the hanging

object is at the desired radius.

8. The speed maintained, stopwatch used to time four revolutions. The time by four

divided and the period recorded in the Table 3.1.

9. The centripetal force varied, the pulley clamped to the track again and different

mass over the pulley hanged. Radius kept constant and the procedure from Step 4

repeated. Total of three different forces done.

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Part 3: Vary Mass (Constant Radius and Force)

1. The object weighed with the additional side masses in place. Mass recorded in

Table 3.5. The object from the side post hanged and the string from the spring

connected to the object. The string passes under the pulley on the center post.

2. The clamp-on pulley attached to the end of the track nearer to the hanging object.

String attached to the hanging object and hangs a known mass over the clamp-on

pulley. This mass recorded in Table3.5. The constant centripetal force established.

3. Radius by aligning the line on the side post with any desired position on the

measuring tape selected. Tighten the thumb screw on the side post while pressing

down on the side post to secure its position. Radius recorded in the Table 3.5.

4. Hanged vertically the object on the side bracket: On the center post, the spring

bracket vertically adjusted until the spring from which the object hangs on the

side post is aligned with the vertical line on the post.

5. The indicator bracket on the center post aligned with the orange indicator.

6. The mass that is hanging over the pulley removed and the pulley removed.

7. Apparatus rotated, the speed increased until the orange indicator centered in the

indicator bracket on the center post. This indicates that the string supporting the

hanging object is once again vertical and thus the hanging object is at the hanging

object is at the desired radius.

8. The speed maintained, stopwatch used to time four revolutions. The time by four

divided and the period recorded in the Table 3.5.

9. The mass of the object varied by removing the side masses. Radius kept constant

and the new period measured. The object weighed again and the mass and period

recorded in Table 3.5.

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APPARATUS

Centripetal force accessory (ME – 8952 )

Stopwatch

Graph paper ( 2 sheets )

String

Rotating platform ( ME – 8951 )

Balance

Mass and hanger set

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RESULTS

PART 1 : VARY RADIUS ( CONSTANT FORCE AND MASS )

Mass of the object = 0.158 kgMass of hanging over the pulley = 0.02 kgSlope of the graph = 1.9 x 10 -4

RADIUS (m) PERIOD ( T ) T2

0.8 0.02 4 x 10-41.45 0.025 6.25 x 10-41.75 0.03 9 x 10-4

TABLE 3.2 : RESULTS ( VARYING RADIUS )

Centripetal Force = mg 0.1962 NCentripetal Force From Slope 1.9 x 10-4

Percent Difference 0.10 %

PART 2 : VARY FORCE ( CONSTANT RADIUS AND MASS )

Mass of object = 0.158 kgRadius = 0.15 mSlope of the graph = 1.38 x 10 -4

MASS OVER PULLEY (kg)

CENTRIPETAL FORCE = mg

PERIOD ( T ) 1/ T2

0.02 kg 0.196 0.025 16000.04 kg 0.392 0.02 25000.06 kg 0.589 0.015 4444

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TABLE 3.3 : VARYING THE CENTRIPETAL FORCE

Mass Of Object ( From Scale ) 0.158 kgMass Of Object ( From Slope ) 1.38 x 10-4 kg

Percent Difference 0.09 %

PART 3 : VARY MASS ( CONSTANT RADIUS AND FORCE )

Mass hanging over pulley = 0.02 kgCentripetal force = mg = 0.196 NRadius = 0.15 m

MASS OF OBJECT ( g )

PERIOD ( T) CALCULATED CENTRIPETAL

FORCE ( N )

PERCENT DIFFERENCE

( % )107.318 g 0.017 2076.5 90.87 158.286 g 0.015 4163.7 95.45209.296 g 0.02 3097.1 93.88

CALCULATION

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Part 1: vary radius (constant force and mass)

Sample 1:

T = 0.02 s

T2 = (0.02)2

= 4 x 10-4 s

Sample 2:

T = 0.025 s

T2 = (0.025)2

= 6.25 x 10-4 s

Sample 3:

T = 0.03 s

T2 = (0.03)2

= 9 x 10-4 s

Centripetal force = mg = (0.02 kg) (9.81 kg m / s2)

= 0.196 N

Percent difference:

( Centripetal force from slope ÷ Centripetal force ) x 100%

= ( 1.9 x 10-4 N ÷ 0.196 N ) x 100%

= 0.10 %

Part 2: vary force (constant radius and mass)

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Sample 1 :

Centripetal Force = mg = (0.02 kg) (9.81 kg m/s2)

= 0.196 N

T = 0.025 s

1 / T2 = 1/ (0.025)2

= 1600 s

Sample 2 :

Centripetal force= mg = (0.04 kg)(9.81 kg/m/s2)

= 0.392 N

T = 0.020 s

1 / T2 = 1 / (0.020)2

= 2500 s

Sample 3 :

Centripetal force = mg= (0.06 kg) (9.81 kg/m/s2)

= 0.589 N

T = 0.015 s

1 / T2 = 1 / (0.015)2

= 4444 s

Percent Difference:

( mass from slope ÷ mass from scale ) x 100%

= ( 1.38 x 10-4 kg ÷ 0.158 kg ) x 100%

= 0.09 %

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Part 3: vary mass (constant radius and force)

Sample 1:

Calculated centripetal force = F= 4п²mr

T²

= 4п² (0.1073) (0.15)

(0.017)²

=2198.6 N

Percent Difference:

[(2198.6 – 189.5) ÷( 2198.6)] x 100 % = 91.38 %

Sample 2:

Calculated centripetal force = F= 4п²mr

T²

= 4п² (0.1582) (0.15)

(0.015)²

= 4163.7 N

Percent Difference:

[( 4163.7 – 189.5 ) ÷ ( 4163.7 )] x 100 % = 95.44 %

Sample 3:

Calculated centripetal force = F= 4п²mr

T²

= 4п² (0.2092) (0.15)

(0.02)²

= 3097.1 N

Percent Difference:

[( 3097.1 – 189.5 ) ÷ ( 3097.1 )] x 100 % = 93.88 %

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DISCUSSIONS

1. When the radius is increased, does the period of rotation increase or decrease?

The period of rotation increase because the larger the radius, the faster the

velocity.

When the radius was increased, the period of rotation will decrease.

2. When the radius and the mass of the rotating object are held constant, does

increasing the period increase or decrease the centripetal force?

When the radius and the mass of the rotating object are held constant, the period

is decrease when increase the centripetal force.

3. As the mass of the object is increase, does the centripetal force increase or

decrease?

If the mass of the object is increase the centripetal force increase.

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CONCLUSION

In conclusion, an object moving in a circle of radius, r at constant speed, v has an

acceleration whose direction is toward the center of the circle and whose magnitude is a =

v2/r. It is not surprising that this acceleration depends on v and r. The greater the speed v,

the faster the velocity changes direction.

RECOMMENDATION

In this experiment, we want the constant of force so that only one person must

rotate the apparatus so that we can get the constant force. The spring bracket vertically

must adjust until the string from which the object hangs on the side post is aligned with

the vertical line on the side post. The string must pass under the pulley on the center post.

Stop watch must been stopped when the person who count finish their counting. Make

sure the object hang rightly so that we can avoid the object from fall while the rotated the

apparatus. Make sure the orange indicator is centered before counting circling.

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REFERENCE

PHYSIC GIANCOLI (SIXTH EDITION)

DOUGLAS C. GIANCOLI

MANUAL LAB

ENGENEERING PYHSICS LABAROTORY (CHE 175)

PROGRAM MATRIKULASI MODUL FIZIK

EDISI PERTAMA 1999

PROF. MADYA DR. ELIAS SAION

PROF MADYA DR. AZIZAN ISMAIL

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APPENDICES

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