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Moment

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Submitted By affiqah
Words 1080
Pages 5
Mechanical Eng. Lab No :1

UNIVERSITI KUALA LUMPUR
MALAYSIA FRANCE INSTITUTE

TITLE: SIMPLE MOMENT EXPERIMENT

1. Objectives

The objectives of the experiments are to demonstrate the equilibrium of moments.

2. Abstract

This report presents the demonstration of the equilibrium of moments using MM 102 simple moments apparatus ESSOM Co. Limited. This equipment provides a simple easy to understand experiment on the equilibrium of moments. Several loads can be put on the beam at various positions. The student has to determine the moment necessary to overcome this rotation and keep the beam level. This experiment is done by putting a specific weight on the load hanger 1 and 3. Weight on load hanger 4 is put and moved until the beam is in equilibrium. The steps are repeated and all the results are jotted down into a table. Based on the results, equilibrium of the beam is influenced by the weight and distance on each hanger.

Figure 1: MM 102 ESSOM Co. Limited

3. Introduction

The purpose of the experiment was to determine the equilibrium of moments. A lever is a simple machine consisting of a beam pivoted at a fixed hinge or fulcrum. The lever arm of a force applied to a solid is the distance from the fulcrum to the line of action of this force. Equilibrium is reached when the algebraic sum of the moments of forces in relation to the fulcrum is zero. The Unit for studying Equilibrium of Moments on a two arm lever provides a simple way of understanding experiments on the equilibrium of moments. The Unit for studying Equilibrium of Moments on a Two Arm Lever (MM102) allows studying the fundamentals of the equilibrium of moments and the application of the law of levers on a two-arm lever. A pivoted beam in the extreme of a vertical support represents a two-arm lever. Several loads can be applied at various positions of the lever with movable weight holders. These loads will make the beam rotate. The equilibrium is attained by moving the loads, and the moment necessary to overcome this rotation and keep the beam level can be determined. The beam is graduated in each direction from the central pivot to read the distances from the pivot point – the lever arms.

The Moment of a force acting about a point or axis is found by multiplying the Force (F) by the perpendicular distance from the axis (d), called the lever arm;

Moment = Force x Perpendicular Distance M = F x d (Nm) = (N) x (m)

When dealing with moments, equilibrium exists when the total moment is zero. (Otherwise it will accelerate in rotation, angular acceleration). Mathematically this is very simple - add the clockwise moments and subtract the anticlockwise ones. For equilibrium of moments;

ΣMo = 0

This report first presents the procedures of the experiment. As the experiment is carried, the results of each different weight are recorded and the counter-clockwise and clockwise moment for this experiment is calculated. In this experiment it will be verified that the sum of the clockwise moments equals the sum of the counterclockwise moments when the applied external forces acting on a rigid object are in static equilibrium. By convention, counter-clockwise moments are assigned a positive sign, while clockwise moments are given a negative sign. Both values are compared and ended with some discussions.

4. Material / Equipment Used :

• MM 102 ESSOM Co. Limited
• Weight

5. Experiment Procedure

O

Figure: 2

When the apparatus is set up as in Figure 2 above, a 4N weight is placed on the load hanger 1 and load hanger 3 with distance 100mm and 50mm respectively. Next, a 2N weight is then placed on the load hanger 4 it is moved until the beam is in equilibrium. The distance d4 is recorded into a table.

After that, the scale is cleared and 4N weight is placed on the load hanger 1 and load hanger 3 with different distance which is 100 and 25 mm, respectively. A 2N weight is placed on the load hanger 4 and it is moved until the beam is in equilibrium. The d4 is recorded.

Finally, all the steps are repeated with different weights and distances.

6. Results

a) Data recorded

Position of Load Hangers and Weight
Left Hand Side of Pin Counter
Clockwise Moment (N.mm) Right Hand Side of Pin Clockwise Moment (N.mm) Percent
Difference

W1
(N) d1
(mm) W3
(N) d3
(mm) W4
(N) d4
(mm)
4 100 400 4 50 2 85 370 -7.80%
4 100 400 4 25 2 130 360 -11%
5 120 600 5 140 3 60 880 38%
2 200 400 2 90 1 165 345 -15%
5 150 750 3 130 2 235 860 14%

b) Calculation

For this experiment, the clockwise and counter clockwise moment and the %difference between moments is calculated.

Moment, M = Force x Distance = (F)(d)

Total moment, ΣMo = 0;
-W1d1 – W3d3 – W4d4 = 0
W4d4 + W3d3 = W1d1
ΣMo clockwise = ΣMo counter clockwise

Mean moment, xM = clockwise moment + counter clockwise moment 2

% difference = clockwise moment - counter clockwise moment mean moment

First data:

ΣMo = 0;
-W1d1 – W3d3 – W4d4 = 0
W4d4 + W3d3 = W1d1
(2N)(85mm) + (4N)(50mm) = (4N)(100mm)
ΣMo clockwise = ΣMo counter clockwise
370N.mm = 400N.mm

xM = 370 + 400 2 = 385

% difference = 370 - 400 385 = -7.80 %

Second data:

ΣMo = 0;
-W1d1 – W3d3 – W4d4 = 0
W4d4 + W3d3 = W1d1
(2N)(130mm) + (4N)(25mm) = (4N)(100mm)
ΣMo clockwise = ΣMo counter clockwise
360N.mm = 600N.mm

xM = 360 + 600 2 = 480

% difference = 360 - 600 480 = -11 %

Third data:

ΣMo = 0;
-W1d1 – W3d3 – W4d4 = 0
W4d4 + W3d3 = W1d1
(3N)(60mm) + (5N)(140mm) = (5N)(120mm)
ΣMo clockwise = ΣMo counter clockwise
880N.mm = 600N.mm

xM = 880 + 600 2 = 740

% difference = 880 - 600 740 = 38 %

Fourth data:

ΣMo = 0;
-W1d1 – W3d3 – W4d4 = 0
W4d4 + W3d3 = W1d1
(1N)(165mm) + (2N)(90mm) = (2N)(200mm)
ΣMo clockwise = ΣMo counter clockwise
345N.mm = 400N.mm

xM = 345 + 400 2 = 372.5

% difference = 345 - 400 372.5 = -15 %

Fifth data:

ΣMo = 0;
-W1d1 – W3d3 – W4d4 = 0
W4d4 + W3d3 = W1d1
(2N)(235mm) + (3N)(130mm)= (5N)(150mm)
ΣMo clockwise = ΣMo counter clockwise
860N.mm = 750N.mm

xM = 860 + 750 2 = 805

% difference = 860 - 750 805 = 14 %

7. Discussion

8. Conclusion

9. References

10. Appendixes

ΣFy = 0
The biggest source of error is positioning things to get the correct balance point. Care, and repeating and averaging are the best options.

Also reduce the percentage errors in the distance measurements by making the distances as large as practical.

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