PHY11L-exp4

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E204: TORQUE: SECOND CONDIION OF EQUILIBRIUM

POLICIOUS, Mark Angelo F.

OBJECTIVE

The Purpose of this experiment is analyzation of

systems in equilibrium and its application, the

effect of torque in system force and the radial

distance on its axis of rotation. Another is to

determine the weights of the pans, force needed

to be in equilibrium and weight of the beam.

Torque is the measurement of force acting on an

object that causes an object to rotate and aside

from the title itself torque plays major role to

complete this experiment.

Other objective of the experiment is to analyze

the systems in equilibrium using the second

condition of equilibrium by Newton and to

distinguish of its uses and significance. The

ability of the body to rotation in a certain

direction is dependent on the torque applied. To

verify this system, three experiments were

performed. A beam is subjected to two balanced

forces perpendicular to it and putting it in

equilibrium state after when a weight force is

applied. The force affecting torque and the

system as well as the rotation equilibrium

applied. Through to this we can conclude that It

is verified and satisfy the principle.

MATERIALS AND METHODS

For this experiment, “Torque: Second condition

of equilibrium”:

The needed materials are model balance

(manufacturer PASCO scientific), a set of mass

loads (manufacturer PASCO scientific), 1 piece of

meter

stick,

a

protractor

(manufacturer

ORIONS), 2 pieces of weight pans (manufacturer

PASCO scientific), a spring balance (manufacturer

DHAUS), and a digital weighing scale.

Figure 1: Complete set of materials

needed in experiment.

In the first piece of the experiment which is the

determining the weights of the pans, the model

balance was set

up in a leveled

table top and the

axis of rotation

was verified in

the middle of the

beam. A weight

pan with a mass

of 24.86 g was

hung to both

side of the beam

and

tried

to

balance. From

then, a 10 gram

mass W1 loaded in the left weight pan and

attempt to make the system in balance by

moving the unloaded weight pan in the right side

near to the rotation of the axis. Patience was

observed as well as the determination due to the

beam that was really sensitive. Do the same

thing of the right weight pan. Load a mass and

try to move the unloaded weight closer to the

center. Moving the two weight pan is necessary

especially if the mass load is getting heavy. The

distance L

1

or L

2

of the weight pan (both side) to

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the center was measured by a ruler to compute

for the P

1

and P

2

using the formulas provided. Do

the same procedures for every trial.

For the second piece of the experiment:

Determining the force needed to be in

equilibrium. Same set

up was use but the

difference

spring

balance is required. To

start with the first a 50

gram mass load was

placed (W

1

) on the left

weight pan of the beam.

The force needed to be

in

equilibrium

was

measured by the spring

balance and verified that the angle was an acute

angle in the horizontal position. The angle of

inclination of the spring balance from the beam

was measured by a protractor and the distance of

the weight pan L

1

and the spring balance L

2

to

the center was measured by a ruler. The

gathered data using the spring balance is the

F

measured

. After which,

force exerted on the

system was computed

using

the

given

formula.

For the second trial,

same mass load was

placed but this time

the spring balance

was on the right side

and

below

the

horizontal

of

the

beam.

Same

procedure was applied and the values gathered

were used to compute for the force applied to the

system.

For the third piece of the experiment:

Determining the weight of the beam. The axis of

rotation was placed on the provided hole. The

weight pan hang on the left side of the beam and

a 50 gram mass load (W

1

) added and placed on

the weight pan and adjusts its position until in

the

state

of

equilibrium. From

then, the distance of

the weight pan on the

new axis of rotation

(L

1

) and the distance

of the former axis of

rotation to the new

axis

(L

2

)

was

measured by a ruler.

The values obtained

was used to compute

for the W

b(computed)

and for W

b(measured)

was done

using a weighing machine to compare the

experimental value to the actual value. Do the

same procedures for each and every trial.

Formulas was already provided to solve readily

after the obtaining the data.

OBSERVATIONS AND RESULTS

In the first part of the experiment: the

determination of the weight of the pans. A

sample computation of weight of the pans for the

first trial is presented below.

( )( )( ) ( )( )( )

( )( ) ( )( )

( )

This table shows the data gathered such as

weights of the pan and distances from the center

to pan.

Table 1. Determining the Weight of Pans

Actual value of pan 1, P1 =24.8 grams Actual value of pan 2, P2 = 24.8 grams

Trial

L

1 (cm) (cm)

L

2 cm)

L

3 (cm)

L

4 (comp)

P

1 (comp)

P

2 1 W1= 10g 13.5 18.7 17.3 14.7 26.86 26.61 W2= 5g 2 W1= 15g 12 19.2 19.8 9.7 24.27 24.55 W2= 25g 3 W1= 30g 6 13 18.5 9.8 23.73 24.80 W2= 20g

Average weight of pan 1, P1= 24.95 g % Difference of P1 = 0.60% Average weight of pan 2, P2= 25.32g % Difference of P2 = 2.07 %

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In the second part of the experiment: the

determination of the force applied needed to be

in equilibrium. A sample computation of force

applied needed to be in equilibrium for the first

trial is presented below.

(

)(

)

(

)

( )( )

( ( ))

This table shows the force applied needed to be

in equilibrium, the distances of the pans from the

axis of rotation and the differences of between

the two trials.

In the third part of the experiment: the

determination the weight of the beam. A sample

computation of weight of the beam for the first

trial is presented below.

(

)(

)

(

)

( )( )

( )

This table shows the weights added on the pans

and the distances of the pans from the new axis

of rotation as well as the new axis of rotation

from the original center of the axis of rotation.

DISCUSSION & CONCLUSION

In the first experiment, the positions of the pans

are changing and moving closer to the axis of

rotation whenever there is a weight loaded in the

pan while in the pan

(no added weight) is farther

to the axis of rotation to make the system in

equilibrium. In conclusion, the heavier the mass

added the closer to its axis of rotation in order to

make the state in equilibrium and vice versa. In

the second part of the experiment, the angle of

the spring balances affects the equilibrium as the

angle increase, the forces decreases and it does

not give an accurate reading because it is done

by hand not a machine. Therefore, equilibrium

still can be achieved but the resulting force

towards to the angle is not as much as accurate.

In the last part of the experiment, getting weight

of the beam, changing the axis of rotation,

change the center of the gravity and as the mass

increases the weight pan is getting closer and

closer to the new axis of rotation.

In the experiment balancing the beam needs

focus, patience and determination. The beam is

sensitive especially the weight pan a little of

unnecessary touch the beam fall. If one of the

groupmate is clumsy, it becomes harder and high

risk of % difference obtained. Another thing,

measuring distance in between the axis of

rotation and the weight can be source of error

and it is because of inaccuracy. Aside from the

fact that we’re human, we can’t tell the whether

the beam is totally levelled, the measurement is

exact and this is the angle needed by using our

own hands. We just assume.

We must observe that the torque is directly

proportional to force which means more force

greater torque and to the force connected to

each system might have equivalent distance from

its axis. Whenever there is more force applied, it

will require less separation from the axis and vice

versa for it to be a rotational equilibrium.

Table 2. Determining the Force needed to be in Equilibrium

Trial

L

1 (cm)

L

2 (cm)

W

1

+P

1 (g)

F

Computed (g)

F

Measured (g)

% diff

1 23.3 7.5 74.8 268.49 280 0.04 % 2 23.8 14.7 74.8 171.7 140 0.2%

TABLE 3. Determining the Weight of the Beam

Trial

L

1 (cm)

L

2 (cm)

W

1

+P

1 (g)

W

B(Computed) (g)

W

B(Measured) (g) 1 13.7 7.5 74.8 136. 63 136.1 2 12.2 7.5 84.8 137.94 3 10.7 7.5 94.8 135.5

Average Weight of Beam, WB = 136.61 g

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In real life application, torque was used and

applied in cars because it is the turning power

and having great torque corresponds to a great

speed and horsepower and also apply off-roads in

which road is bumpy and not levelled.

ACKNOWLEDGMENT & REFERENCE

I would like to thank my group mates for a job

well done. For Christel Lopez, who always ready

in taking picture and uploading right away on

that day. Isabel Salvo, accuracy in getting

measurement of every trail of experiment. Nick

Fernandez, for his MacBook and mastery in doing

excels. An Soung Man, courtesy in the

experiment. Zueleta and also myself, for doing

the sample computations after performing the

experiment. Our teamwork would is undeniably

the key on having a commendable results. I

would not have done this experiment by myself.

Thank you.

I would like to acknowledge the lab assistants for

lending us the laboratory apparatuses as well as

their politeness. Next, I would like to thank Prof.

Ricardo De Leon for sharing us the quiz results

and making us nervous. It was a tough for me for

having that result but it doesn’t mean I give up.

Again, thank you sir.

And especially, I would like to thank Almighty

God for giving me the knowledge, and the

wisdom in writing this laboratory report also the

previous lab reports.

Sources:



http://adventure.howstuffworks.com/outd

oor-activities/off-roading/torque-off-roading.htm



http://lofi.forum.physorg.com/Torque_12

718.html



https://secure.drivers.lexus.com/lexusdriv

ers/magazine/articles/Vehicle-Insider/Horsepower-vs-Torque



http://www.britannica.com/EBchecked/to

pic/600049/torque



http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html



Walker, J., Halliday, D., & Resnick, R.

(2014). Principles of Physics. 10th Edition.

262-264.