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Report 5: Pulley and Centripetal Acceleration

Title:

Simple Machine and Centripetal Acceleration

Laboratorial Report 6

Created to fulfill the assignment for Mechanic and heat EN222 subject

By:

Debby Syefira

Damavara

I Wayan Surya Aryana

Reyhan

Lecturers:

Lina J Diguna

Fatih

Sampoerna University

Performed: Jakarta, June 19th, 2015


Abstract

The sixth physics activity is testing the concept of simple machine and centripetal

acceleration. This experimental activity is instructing student to be able to construct a simple machine using pulley rigged with string. By using the formula given in the theory, the experiment

is resulting the mechanical advantages whether in the single fixed pulley, single movable pulley,

or double pulleys. Besides mechanical advantages, the data gotten in the observation will also being used to determine the work and efficiency of the system of the pulley. Centripetal

acceleration, as the second activity besides simple machine, is also undergone. By assemble the centripetal apparatus, the student is observing the force involved in the rotational motion. The

centripetal acceleration is basically collecting the data observation by varying the variable that is

determining the centripetal itself. In the last of the observation, the student is expected to be able to explore and graph the relationship among the velocity, centripetal force, and the radius of the

circular path of an object undergoing constant circular motion.

Keywords: Pulley, Spring, Force, Mechanical Advantage, Velocity, and Centripetal Force.


CHAPTER I

OBJECTIVES

The objective of this experiment are:

Investigating the properties of a pulley and its use as a simple machine.

Calculating the angular velocity of a spinning object using varying hanging and rotational

masses and varying radii.

Calculating the theoretical centripetal force.

Calculating the experimental centripetal force.

Graphing and analyze experimental data.


CHAPTER II

METHODOLOGY

2.1 Materials

The materials that are being used in the experiment are divided two types as follow:

Materials of Simple Machine Experiment – Pulleys Practicum

Table 1. Simple Machine Material

Materials from Label or box/bag Quantity Item description

Student provides

1 Support for pulleys

1 Small plastic bag

1 Coins or washers for

weights

From LabPaq

2 Pulley

1 Scale-spring-500g

1 Tape measure, 3m

Dissection tray Misc supplies PK-W 1 String

Material of Centripetal Acceleration Experiment

1. Centripetal force apparatus, including : glass rod, steel washers (20), paperclips (2),

rubber stopper (2 holes), thread (4 m)

2. Scale spring 500 g

3. Stopwatch digital

4. Tape measure 3 m

2.2 Procedures

Since in the experiment are consisting of four different activities, therefore the procedure are

divided into four parts as follow:

Activity 1: Simple Machine (Pulley Experiment)

1. Find a suitable horizontal support from which to freely hang your pulleys. It is important

that the pulley assembly hangs freely, that the observer is able to read and record the

measurements from the spring scale, and that the assembly does not rest against anything.


2. The student should make a weight bag to use as the mass. Place coins or washers that

make a force of less than 4.9 N (500g) inside a small plastic bag.

3. Record the bag’s weight in Data Table 2 as resistance. (Remember that you can use the

equation weight = mass x gravitational acceleration to convert from grams of mass to

newton of force). Tie a piece of string around the top of the bag so the weights do not fall

out and suspend the bag as shown in the following experiment diagrams.

4. Single Fixed Pulley (IMA = 1)

a. Suspend a single fixed pulley from a support by tying a string from the support to the

pulley as shown at below.

b. Pass a second single string through the pulley. At the bottom end of the string attach

the weight bag and at the other end of the string attach the spring scale.

c. Start with the weight bag suspended off the ground. Note the exact location of the bag

and the scale. Pull on the scale until the weight bag rises 10cm from its starting point.

Report this as the resistance distance.

d. Read the scale and record this as the effort. Record the effort distance, which is the

distance the scale moved.

5. Single Moveable Pulley (IMA = 2)

a. Pass a single string through the pulley as shown in figure below. Attach one end of

the string to the support and the other end to the spring scale. Attach the weight bag

directly to the bottom of the pulley. Note the exact location of both the bag and the

scale, and record the scale reading.

b. Lift the weight bag by lifting the scale. Measure the distance that the resistance

moves and record this as the resistance distance. Measure the distance that the scale

moved and record this as the effort distance.

6. Double Pulley (IMA = 2)

a. Tie one pulley directly to the support. Tie the end of a string to the end of that pulley.

Run the other end of the string around a second pulley end then up and around the

first pulley. Tie this end of the scale. Attach the weight bag to the lower pulley.

b. Lift the weight bag off the ground some distance and note the exact location of the

bag and the scale. Pull the scale to lift the weight farther; measure and record that


resistance distance. Read the scale and record this effort force. Measure and record

the distance that the scale moves, the effort distance.

Activity 2: Cart Calibration (Measuring the Spring Constant)

Warning : Choose an area that is free from obstructions and breakable objects.

1. Record the number of washers from the kit in Data Table 2. Place all of the washers into a

bag to weigh their mass and record the total mass in Data Table 2. Find the average mass

of each washers in kilograms and record it in Data Table 2.

Table 2. Mass of Washers and Rubber Stopper

Item Value

Mass of rubber stopper

Mass of all washers combined (kg)

Number of washers

Average mass of each washer (kg)

2. Assemble the centripetal apparatus

a. Pull out the 4 m of string provided in the apparatus kit

b. Before threading the string through the glass rod, make sure the smooth end of the glass

rod is at the top nearest the rotating rubber stopper.

c. Tie the rubber stopper to the end of the string and thread the other end of the string

through the plastic-covered glass rod

Figures 3. Double Pulley Figures 2. Single Moveable

Pulley

Figures 1. Single Fix Pulley

Double Pulley


d. Thread about 30 g of washers onto the end of the string opposite from the stopper.

Record this constant hanging mass in the line above Data Table 3.

Table 3. Varying Radius Data

A B C = B/10 D = 2𝝅 x A E = D/C F = E²

Radius

(m)

Time (s)

10 rev

Time (s)

1 rev

Circumference

2𝝅r (m)

Velocity

( 𝐦

𝐬 )

(Velocity)²

( 𝐦²

𝐬² )

Trial 1

Trial 2

Trial 3

Trial 4

e. Tie the washer-end of the string to a paper clip, and if needed spread open the paper

clip to ensure that the washers do not fly off the apparatus.

f. Tie the paper clip about 20 cm above the washers.

3. Pull the string through the glass rod so that approximately 0.7 m of the string is between

the glass rod and stopper. Practice swinging the stopper around in a circle over head, while

holding onto the glass rod. Support the suspended mass containing the washers with one

hand and hold the rod in the other. Be careful and review the safety precautions at the

beginning of this procedure.

4. Swing the stopper in a circular motion. Slowly release the hanging mass and adjust the

rotating speed of the stopper so that the paper clip attached to the string above the washers

stays a few centimeters below the bottom of the tube, neither rising nor falling.

5. Stop spinning the rubber stopper and use the measuring tape to measure the length of the

string in meters. This is the length of the string between the glass tube and rubber stopper.

Record this length as the radius for trial 1 in Data Table 3.

6. Once we are able to spin the stopper with a steady pace, we can begin the experimental

portion of the lab.

7. Begin to spin the apparatus, maintaining a constant radius. After the spin is stabilized, have

an assistant use a stopwatch to time (in seconds) 10 revolutions. Record this 10 rev time

for Trial 1 in Data Table 3.

8. Shorten the length of string between the stopper and the top of the glass tube by

approximately 10 cm. Pull the string through the bottom of the glass tube to shorten the

distance L between the top of the glass tube and the stopper. Use the tape measure to record


this new length between the top of the glass rod and the stopper as the radius for Trial 2 in

Data Table 3.

9. Repeat the procedure of swinging the stopper for 10 revolutions while it is being timed.

Record the time for 10 rev in Data Table 3 for Trial 2.

10. Shorten the string by another 10 cm as in step 7, and record this new radius in Data Table

3 for Trial 3.



12. Shorten the string by another 10 cm as in step 7, and record this new radius in Data Table

3 for Trial 4.



14. Complete the calculations for columns C through F later in Exercise 3.

Activity 3: Fixed Radius-Varying Hanging Mass

1. Because a radius of 50 cm and a hanging mass of approximately 30 g were used in one of

the trials in exercise 1, record the results from that trial under Trial 1 in Data Table 4

Table 4. Varying Hanging Mass Data

A B C = B/10 D = 2𝝅 x A E = D/C F = E²

Hanging

mass

(kg)

Radius

(m)

Time (s)

10 rev

Time (s)

1 rev

Circumference

2𝝅r (m)

Velocity

( 𝐦

𝐬 )

(Velocity)²

( 𝐦²

𝐬² )

Trial 1

Trial 2

Trial 3

Trial 4

2. Adjust the radius of the rotating mass to 0.5 m. Because this value will remain the same

for this part of the experiment, record the length of the radius in Data Table 4 for Trial 1

through 4.

3. Change the number of hanging washers so that they weigh approximately 40 g. Record this

hanging mass in Data Table 4 for Trial 2. Record the mass of the stopper in Data Table 4.

Use the mass for the stopper from Data Table 1.


4. Use this 40 g hanging mass to perform one trial of 10 rev in a manner similar to that in

Exercise 1. Record the time in Data Table 4 for Trial 2.

5. Add more washers until the hanging mass is approximately 50 g. Record this hanging mass

in Data Table 4 for Trial 3.



7. Add more washers until the hanging mass is approximately 60 g. Record this hanging mass

in Data Table 4 for Trial 4.



9. Complete the calculations for columns C through F after Exercise 3.

Activity 4: Fixed Radius-Varying Rotating Mass

1. Because a radius of 50 cm and a hanging mass of approximately 50 g were used in Trial 3

of exercise 2, record the results from that trial under Trial 1 in Data Table 5.

Table 5. : Varying Rotating Mass Data

A B C = B/10 D = 2𝝅 x A E = D/C F = 1/E²

Rotating

mass

(kg)

Radius

(m)

Time (s)

10 rev

Time (s)

1 rev

Circumference

2𝝅r (m)

Velocity

( 𝐦

𝐬 )

1/(Velocity)²

( 𝐬²

𝐦² )

Trial 1

Trial 2

Trial 3

Trial 4

2. Use a hanging mass of approximately 50 g and record it as the constant hanging mass for

Data Table 5. Use the radius at its current length of 0.5 m and record this value into Data

Table 5 for Trials 1 through 4.

3. Untie the string attached to the stopper. (if the knot cannot be easily untied, cut the knot

and re-adjust the string) Tie two washers together with the stopper. Add the average mass

of two washers to the mass of the rubber stopper and record this total rotating mass un Data

Table 5 for trial 2. In each step where we add washers, make sure that we re-tie the knot

securely to ensure the weights do not fly off the string.


4. Use this rotating mass to perform one trial of 10 revolutions in a manner similar to the

process in part 1. Record the time in Data Table 5 for trial 2.

5. Add an additional two washers to the rotating mass. Recalculate the new rotating mass,

and record it in Data Table 5 for trial 3.

6. Use this rotating mass to perform one trial of 10 revolutions in a manner similar to that in

part 1. Record the time for 10 rev in Data Table 5 for trial 3.

7. Add an additional two washers to the rotating mass. Recalculate the new rotating mass,

and record it in Data Table 5 for trial 4.

8. Use this rotating mass to perform one trial of 10 revolutions in a manner similar to that in

part 1. Record the time for 10 rev in Data Table 5 for trial 4.


CHAPTER III

RESULT AND DISCUSSION

3.1 Theory

Theory of Simple Machine – Pulleys Practicum

A pulley is defined as being one of the three simple machines: the pulley, the lever, and the

inclined plane. The purpose of a machine is to help accomplish the term physicists describe as

work. While the rest of us may casually refer to work as any exertion of effort toward a goal,

physicists have a very specific idea of work. It is defined as the force applied to an object multiplied

by the distance that object is moved. (McDunnigan, n.d.) Moreover, the pulleys are divided into

three types of pulley which are fixed pulley, moveable pulley and compound pulley.

A fixed pulley describes a pulley that is secured to a single spot. While the pulley's wheel

will turn with the rope or chord that passes through it, the pulley itself will remain stationary.

Because of this, the force exerted on the object on the opposite side of the pulley will be exactly

the amount of force applied on the user's side of the pulley. This is described as having a

mechanical advantage of one, because the amount of force you apply is precisely the amount of

force the machine will exert on the object you are trying to move. (McDunnigan, n.d.)

A movable pulley is a pulley that moves with the load you are moving, as opposed to a fixed

pulley which does not move. However, unlike the fixed pulley which exerts only as much force on

the object being moved as is applied to the machine, a movable pulley will multiple the force which

the user applies to the machine in doing work on an object. This means that less force must be

applied by the user to do the same amount of work, effectively making the work what might be

described as "easier." (McDunnigan, n.d.)

For example, if a man was using a fixed pulley to lift a box then he must apply a force which

overcomes the force of gravity on the box. Since the fixed pulley does not multiply force, this

means he must apply that amount of force himself. In contrast, if he was using a movable pulley,

which does multiply force, then he would only have to apply a fraction of the force necessary to


overcome gravity, and the machine would multiply that into the sufficient amount. (McDunnigan,

n.d.)

The third type of pulley is the compound pulley. The compound pulley or double pulley

system is a combination of fixed and movable pulleys. While this system has the greatest

multiplication of user force, the system itself takes up space and involves moving the object a

longer distance. (McDunnigan, n.d.)

The Principle Centripetal Acceleration

“Uniform circular motion can be described as the motion of an object in a circle at a

constant speed. As an object moves in a circle, it is constantly changing its direction. At all

instances, the object is moving tangent to the circle. Since the direction of the velocity vector is

the same as the direction of the object's motion, the velocity vector is directed tangent to the circle

as well.” (Classroom, 2015)

Centripetal acceleration is the rate of change of tangential velocity:

=

Note:

The direction of the centripetal acceleration is always inwards along the radius vector of

the circular motion.

The magnitude of the centripetal acceleration is related to the tangential speed and angular

velocity as follows:

ac = = r

In general, a particle moving in a circle experiences both angular acceleration and

centripetal acceleration. Since the two are always perpendicular, by definition, the

magnitude of the net acceleration a total is:

a total = =


(Centripetal Acceleration, 2015)

Newton’s first and second laws of motion state that an object moves at a constant speed in

a straight line unless an external force act upon that object and that a force cause an object’s

acceleration. By following these laws, the force on a circular moving object is called centripetal

force. Centripetal force accelerates an object by changing the direction of its velocity without

changing its speed.

Mathematically, centripetal acceleration and centripetal force are represented as:

Centripetal acceleration: Centripetal force:

Ac = 𝑣²

𝑟 Fc =

𝑚𝑣²

𝑟

Ac represent centripetal acceleration Fc represent centripetal force

V represent velocity m represent object’s mass

R represent radius of circle r represent radius of circle

There are two different ways to measure a rotational angle𝜃: degrees and radians. A

revolution (rev) is defined as one complete turn, and one complete turn is defined to be 360˚. Thus,

1 rev = 360˚. A radian measure is the ratio of two important length : the radius r and the arc length

s. Thus, 𝜃 = s/r.

One radian (rad) is the angle subtended from the center of a circle by an arc whose length

is equal to the radius of the circle. Thus, 2𝜋 rad = 360˚, and 1 rad = 360/2𝜋 = 57.3˚.


In this experiment the rubber stopper is connected to a string and is rotated in a horizontal

circle. The tension in the string causes the stopper to undergo centripetal acceleration.

- Circumference of the circle = distance of 1 rev = 2𝜋r

- T = time required for one complete evolution

- Velocity of the rotational object = distance traveled/time = 2𝜋𝑟

Τ

Thus, the centripetal force that must be supplied is

𝐹𝑐 = 𝑚𝑣²

𝑟

And, the centripetal acceleration is:

𝑎𝑐 = 𝑣²

𝑟= 𝑎𝑐 =

(2𝜋𝑟²

𝑇)

𝑟=

4𝜋²𝑟

𝑇²

In addition to centripetal acceleration, the force of gravity acts on the rubber stopper as it

is whirled along a horizontal plane. Because gravity acts perpendicular to the centripetal force, the

orbital plane of the rotating mass lies below the horizontal plane at the top end of the vertical tube.

Therefore, the orbital radius is less than the distance L between the end of the glass tube and the

center of mass of the rotating weight. The orbital radius is actually L sin𝜃, where 𝜃 is the angle,

the string makes with the glass tube.

Despite these factors, the data obtained from this experiment should be reasonable

approximations that demonstrate the basic relationships among the variables.

To calculate Theoretical centripetal force:

𝐹𝑐 = ℎ𝑎𝑛𝑔𝑖𝑛𝑔 𝑚𝑎𝑠𝑠 𝑥 𝑔 (9.81)

To calculate the experimental force:

𝐹𝑐 = 𝑟𝑜𝑡𝑎𝑡𝑖𝑛𝑔 𝑚𝑎𝑠𝑠 𝑥 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦²

𝑟𝑎𝑑𝑖𝑢𝑠


3.2 Discussion 1: Simple Machine (Pulley Experiment)

Table 6. Data Record of the Pulley Experiment

Fixed Pulley Movable Pulley Double Pulley Effort (g or N) 2.1 1.3 N 0.97 N

Effort Distance (m) 0.1 0.18 m 0.22 m

Resistance (g or N) 2.45 2.4696 N 2.4696 N

Resistance Distance (m) 0.1 0.10 m 0.10 m

Work in (N.m) 0.21 0.234 N.m 0.2134 N.m

Work out (N.m) 0.245 0.24696 N.m 0.24696 N.m

Efficiency 117% 105.54% 115.73% Mechanical Advantage 1.167 1.899 2.54

The data shown above is the way the student to verify the theory that works on a pulley. As

stated in the procedures, the IMA for the pulley is different based on the type of the pulley. The

IMA of a fixed pulley is 1, where the amount of effort distance should be in the ratio of 1:1 with

the resistance distance. The IMA of a moveable pulley is 1, where the amount of effort distance

should also be in the ratio of 1:1 with the resistance distance as well as works in fixed pulley. The

IMA of a double pulley is 2, where the amount of effort distance should be in the ratio of 1:2 with

the resistance distance.

Fixed Pulley

By using the table above, student could observed the work of fixed pulley. According to

the table above, student found that the value of effort and resistance is the same for the fixed pulley.

Also, the effort distance and the resistance distance in the fixed pulley is almost the same as it is

almost create a ratio of 1:1. Furthermore, the efficiency of the fixed pulley is 117% means that

there was not a present of energy lose from this mechanism. This mechanism works efficiently.

Moreover, the mechanical advantage of this type of pulley is 1.167. If it is rounded to the tenth, it

would give a result of 1. Even though this mechanism give advantage as its give a result of 1 for

the mechanism advantage, this could not help the human that much. That is because this

mechanism could not double the result of work out as the work in is given.


Movable Pulley

Based on the data that have been gotten which are the value of effort, effort distance,

resistance, and resistance distance, the value of workin and the value of workout in which the student

needs to determine can consequently be calculated as follow:

𝑊𝑜𝑟𝑘 𝑖𝑛 = 𝐸𝑓𝑓𝑜𝑟𝑡 × 𝐸𝑓𝑓𝑜𝑟𝑡 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑊𝑜𝑟𝑘 𝑖𝑛 = 1.3 N × 0.18 m

𝑊𝑜𝑟𝑘 𝑖𝑛 = 0.234 N. m

𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 × 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 = 2.4696 N × 0.10 m

𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 = 0.24696 N. m

The value of the work in and the value of the workout, based on the theory, then can be used to

determine both efficiency of the pulley system and the mechanical advantage that the pulley system

give s to the user. The calculation to find the efficiency and mechanical advantage are as follow:

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑊 𝑜𝑢𝑡

𝑊 𝑖𝑛

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 0.24696 N. m

O. 234 N. m× 100%

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 105.54%

𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 𝐹 𝑜𝑢𝑡

𝐹 𝑖𝑛

𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 2.4696 𝑁

1.3 𝑁

𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 1.899

This result, experimental mechanical advantage, is basically showing that the movable pulley

is a device that can helping out the people. Movable pulley can change the weight of an object up

to half of its initial weight (F ≈ 1

2 ).


Double Pulley

In the last pulley activities, the double pulley is being tested; this pulley experiment, as what

it is shown in the table above, is determining the value of the work in, the value of workout,

efficiency, and the mechanical advantage. By the observation data in which they are effort, effort

distance, resistance, and the resistance distance, the workin then can be calculated as follow:

𝑊𝑜𝑟𝑘 𝑖𝑛 = 𝐸𝑓𝑓𝑜𝑟𝑡 × 𝐸𝑓𝑓𝑜𝑟𝑡 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑊𝑜𝑟𝑘 𝑖𝑛 = 0.97 N × 0.22 m

𝑊𝑜𝑟𝑘 𝑖𝑛 = 0.2134 N. m

Besides the workin value, the workout value in which it is the work that is done by the load of

object can be calculated as follow:

𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 × 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 = 2.4696 N × 0.10 m

𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 = 0.24696 𝑁. 𝑚

After finding the value of both workin and workout, the efficiency consequently can be

calculated as follow:

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑊 𝑜𝑢𝑡

𝑊 𝑖𝑛

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 0.24696 𝑁. 𝑚

0.2134 N. m× 100%

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 115.73%

By using the value of Fout and Fin in which they are respectively resistance and effort, the

mechanical advantage in which it is the relative comparison advantage of a certain pulley can

consequently be determined as follow:

𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 𝐹 𝑜𝑢𝑡

𝐹 𝑖𝑛

𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 2.4696 N

0.97 N

𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 2.54


3.3 Discussion 2: Centripetal Acceleration

Table 7. Mass of Washers and Rubber Stopper

Item Value

Mass of rubber stopper 0.017 kg

Mass of all washers combined (kg) 0.1 kg

Number of washers 10 pcs

Average mass of each washer (kg) 0.01 kg

Constant Hanging Mass = 0.1 kg

Constant Rotating Mass = 0.017 kg


A B C = B/10 D = 2𝝅 x A E = D/C F = E²

Radius

(m)

Time (s)

10 rev

Time (s)

1 rev

Circumference

2𝝅r (m)

Velocity

( 𝐦

𝐬 )

(Velocity)²

( 𝐦²

𝐬² )

Trial 1 0.18 3.28 0.328 1.13 3.45 11.9

Trial 2 0.545 4.54 0.454 3.42 7.53 56.7

Trial 3 0.29 4.11 0.411 1.82 4.43 19.6

Trial 4 0.25 4.05 0.405 1.57 3.88 15.0

Constant Rotating Mass = 0.017 kg


Table 9. Varying hanging mass data

A B C = B/10 D = 2𝝅 x A E = D/C F = E²

Hanging

mass

(kg)

Radius

(m)

Time (s)

10 rev

Time (s)

1 rev

Circumference

2𝝅r (m)

Velocity

( 𝐦

𝐬 )

(Velocity)²

( 𝐦²

𝐬² )

Trial 1 0.1 0.3 4.3 0.43 1.88 4.37 19.12

Trial 2 0.12 0.3 3.63 0.363 1.88 5.18 26.82

Trial 3 0.14 0.3 3.59 0.359 1.88 5.24 27.42

Trial 4 0.19 0.3 3.2 0.32 1.88 5.88 34.52

Constant Hanging Mass = 0.1 kg

Table 10. Varying Rotating Mass Data

Data Table 4 : Varying rotating mass data

A B C = B/10 D = 2𝝅 x A E = D/C F = 1/E²

Rotating

mass

(kg)

Radius

(m)

Time (s)

10 rev

Time (s)

1 rev

Circumference

2𝝅r (m)

Velocity

( 𝐦

𝐬 )

1/(Velocity)²

( 𝐬²

𝐦² )

Trial 1 0.017 0.317 3.24 0.32 1.99 6.1 0.03

Trial 2 0.025 0.317 5.15 0.52 1.99 3.9 0.07

Trial 3 0.034 0.317 6.02 0.60 1.99 3.3 0.09

Trial 4 0.044 0.317 6.23 0.62 1.99 3.2 0.10


Data Table 5: Varying Radius Data

Theoretical Fc (N) Velocity²/radius Experimental Fc (N) %Error

Trial 1 0.981 65.94 1.12 0.143

Trial 2 0.981 104.12 1.77 0.804

Trial 3 0.981 67.62 1.15 0.172

Trial 4 0.981 60.11 1.02 0.042


Table 12. Varying Hanging Mass Data


Trial 1 0.98 63.7 1.08 0.104

Trial 2 1.18 89.4 1.52 0.291

Trial 3 1.37 91.4 1.55 0.132

Trial 4 1.86 115.1 1.96 0.049

Table 13. Varying Rotating Mass Data


Trial 1 0.981 119 2.02 1.06

Trial 2 0.981 47 1.18 0.20

Trial 3 0.981 34 1.17 0.19

Trial 4 0.981 32 1.42 0.44


Graph from Table 8

11,9

56,7

19,6

15,0

0,0

10,0

20,0

30,0

40,0

50,0

60,0

0,18 0,545 0,29 0,25

velo

city

²

Radius

Radius vs velocity squared

3,45

7,53

4,43

3,88

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

0,18 0,545 0,29 0,25

Vel

oci

ty

Radius

Radius vs Velocity


Graph from table 9

0,000

0,500

1,000

1,500

2,000

2,500

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Cen

trip

etal

Fo

rce

Velocity

Velocity vs Centripetal force

0,000

0,500

1,000

1,500

2,000

2,500

0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00

Cen

trip

etal

Fo

rce

Velocity²

Velocity squared vs centripetal force


Graph from table 10

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 0,05

Vel

oci

ty

Rotating Mass

Rotating Mass vs Velocity

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 0,05

1/ v

elo

city

sq

uar

ed

Rotating mass

Rotating mass vs 1/velocity squared


CHAPTER IV

CONCLUSION

4.1 Conclusion

Simple fixed pulley has mechanical advantage equal to one; simple movable pulley has

mechanical advantage equal to two; and double pulley has mechanical advantage equal to

2.

The value of the theoretical centripetal force and experimental centripetal force are shown

in the table 11, table 12, and table 13.

The graph of the centripetal acceleration activity is shown in the discussion 2.

4.2 Recommendation

1. Make sure all of the equipment in right precision and accuracy.

2. Record the data more than one to compare the result, especially if it is related to time. Let

at least two people count the time.

3. The improvement of the number of the apparatus to allow student to have longer time to

do the observation

4. The lab assistance should understand well the procedure of the experiment in order the help

the student to keep on the track of the activity


REFERENCES

Centripetal Acceleration. (2015, June 21). Retrieved from Theory.uwinnipeg.ca:

http://theory.uwinnipeg.ca/physics/circ/node6.html

Classroom, T. P. (2015, June 21). Uniform Circular Motion. Retrieved from The Physics Classroom:

http://www.physicsclassroom.com/mmedia/circmot/ucm.cfm

McDunnigan, M. (n.d.). 3 Types of Pulleys (with picture) | eHow. Retrieved June 21, 2015, from eHow:

http://www.ehow.com/list_7319525_3-types-pulleys.html

http://www.ehow.com/list_7319525_3-types-pulleys.html

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