Abu Dhabi Men’s College

Statics & DynamicsEMCH N202

Hasan Mohammed Maanna

H00214183

CIA

Laboratory Experiment

Balancing Forces

Non Concurrent Forces / The Principle of Moments

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Table of Contents

1. Introduction

2. Materials

3. Procedure Part A Part B

4. Results Part A Part B

5. Discussion

6. Conclusion

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1. Introduction:

In this laboratory experiment we are going to the forces to be in equilibrium the moment arm in the Left = moment in the right. Moment is the turning effect that acts on an object to turn either clockwise or counterclockwise direction.

In this experiment we are going to demonstrate the law of moments on different masses (Force) and distance from the pivot and then we are going to apply the formula to calculate the force exerted by the mass and calculate the moment.

Force = m x g

Where m is the mass and g is the acceleration due to gravity (9.8 m/s²)

Moment = F x d

Where F is the force exerted from the object mass and d is the distance from the pivot.

2. Materials:

a. Meter Ruleb. Different mass object that are enough to have at least three trialsc. A fulcrum.

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3. Procedure:-

Part A:

First place pivot at the rule’s center of gravity, making sure the rule is balanced (in Equilibrium).

Choose two different masses (m1, m2) and record their weight in the data table.

Place the weights on the left and right sides of the rule with different distances from its center.

Keep changing the distance of one of the weights until the rule is in Equilibrium.

Record the distances of the weights from the center of the rule in meters.

Calculate the moment at the fulcrum by using the formula given above (M1 = m1 x g x d1) or (M1 = F1d1)

Record the data respectively in the table.

Repeat step No.: 6 to calculate M2 (M2 = m2 x g x d2)

After calculating moment for both sides (M1 & M2), calculate

the Percentage of Error by ℑ2−M 1 IM 2

(100) to find the percentage

of error (Should be bellow 5%).

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Part B:

First place pivot at the rule’s center of gravity, making sure the rule is balanced (in Equilibrium).

Choose two different masses (m1, m2) and record their weight in the data table.

Place the weights on the left and right sides of the rule with different distances from its center.

Keep changing the distance and angle of one of the weights until the rule is in Equilibrium (Rule is not parallel with the surface).

Record the distances of the weights from the center of the rule in meters.

Record the angle at which the rule is in Equilibrium.

Calculate the moment at the fulcrum by using the formula given above (M1 = m1 x g x d1) or (M1 = F1d1).

Record the data respectively in the table.

Repeat step No.: 7 to calculate M2 (M2 = m2 x g x d2).

After calculating moment for both sides (M1 & M2), calculate

the Percentage of Error by ℑ2−M 1 IM 2

(100) to find the percentage of error (Should be bellow 5%).

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Part A: Rule Parallel with the

surface.

Part B: Rule at an Angle

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4. Data Tables:-

Part A:

DATA TABLE (PART A)

Trial m1

(grams)d1

(meters)M1

(Nm)m2

(grams)d2

(meters)M2

(Nm) Error %

1 73 0.3 0.215 69 0.325 0.220 2.30%

2 83 0.3 0.244 79 0.325 0.252 3.02%

3 83 0.163 0.133 50 0.28 0.137 3.38%

Part B:

DATA TABLE (PART B)

Trial

m1

(grams)d1

(meters)M1

(Nm)m2

(grams)d2

(meters)M2

(Nm)Angle

(θ) Error %

1 150 0.36 0.137 200 0.28 0.143 15° 3.60%

2 55 0.44 0.136 108 0.22 0.134 35° 1.5%

3 74.5 0.32 0.041 112 0.22 0.042 10° 3.30%

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5. Discussion:-

Part A:In this experiment we hanged two weights with different masses on the Left & right hand sides of the rule. Then we adjusted the weights at different distances from the fulcrum. Our aim was to keep the rule as close as possible to be parallel with the surface to proof that the law of moment is true.After making it equilibrium we calculated the moment as I’ll show in Figure 1.

Figure 1

d1 d2

m1 m2

The Moment is calculated by (M = m x g x d), moment of each side is calculated separately with its respective components.

Bellow is the results we got from one of the trials:

M1 = 0.073 x9.81x 0.3 = 0.215 Nm

M2 = 0.069 x 9.81 x 0.325 = 0.220 Nm

∑M = M2 – M1

∑M = 0.220 – 0.215 = 0.005 Nm

Error % = 2.3%

The results agree with the Moment Equilibrium Rule.

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Part B:

In this experiment we hanged two weights with different masses on the Left & right hand sides of the rule. Then we adjusted the weights at different distances from the fulcrum. Our aim was to keep the rule at an angle with the surface to proof that the law of moment equilibrium is true.After making it equilibrium we calculated the moment as I’ll show in Figure 2.

Figure 2

d1

d2

m1

m2

In Figure 2 it shows that the rule is tilted to an angle from its center of gravity that is supported by the fulcrum.

For the rule to be in equilibrium moments on both sides have to act inversely on each other, which means that one must cancel the other so that we reach a point stating that ∑M = 0 when both ML

and MR are added together. I am going to prove this by applying the Moment Equilibrium Rule to one of the results provided at the begging of this report.

M1 = 0.055 x 9.81 x 0.44 x sin (35°) = 0.136 NmM2 = 0.108 x 9.81 x 0.22 x sin (35°) = 0.134 Nm∑M = M2 – M1∑M = 0.134 – 0.136 = - 0.002 NmError % = 1.5 %The results agree with the Moment Equilibrium Rule.

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6. Conclusion:

In this experiment we have proved that for a system to be in Equilibrium moments on clockwise and counterclockwise have to be equal so that when they are added the sum of them must be equal to zero, although we have found some errors, but we have proved that the Moment Equilibrium Rule is true after experimenting it in two different scenarios (Part A & B).

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