# lab report 2

Student name JunJie Liu

Student ID 1512042

Experiment Date 11 Feb 2015

Lab group Mech 7

Introduction

In this lab report we show the basic methods of measuring centrifugal force using two counter balanced bell-cranks spin on a turntable (shows in figure 1) and able to calculate the centrifugal force with given conditions shows in figure 1.

*Figure 1 (University of Birmingham. Experiments and Statistics, 2014.) Objectives

1. To calculate bending moment at the “cut” using displayed force (figure 1) times the perpendicular distance between the load cell and the “cut” and see its agreement with the theory. Bending moment =Applied Load X Distance (eq. 1)

2. To examine the relationship of bending moment, loading and cut positions for given set of conditions. 3. To examine whether the bending moment at the ‘cut’ equal to the algebraic sum of moment of force acing to the left or right of the ‘cut’.

Observations and Results

The experiment was done in two parts and the results for individual part are showed below separately. Part 1

The Experimental Bending moment was obtained by multiply the displayed force and perpendicular distance between load cell and the “cut” (moment arm) and the perpendicular distance between load cell and the “cut” is 0.125m throughout the experiment. The Load was obtained by multiply Mass in Kg and gravity which is 9.81. The Theoretical Bending moment was obtained by substituting calculated loads in table 1 into equation 2 where the respected quantities can be seen in figure 2. The Percentage Error was calculated by using the difference between Experimental value and Theoretical value divide by Theoretical and times a hundred.

Part 2

Figure 6: Graph of Bending Moment for Figure 5

Discussion

As the experiment was done by two parts, discussion is done separately for individual parts. Part 1

To derive equation 2

Taking the moment at RB Total moment equal to 0

RA*l=W*(l-a) RA = W*(l-a)/l (eq.3)

Substitute (eq.3) into (eq.1) simplify the equation to get eq.2 To achieve the objectives of the lab graph was plotted using Experimental Bending moment against Theoretical Bending moment in experiment 1(Figure 7).From the graph we are able to see a strong linear relationship which is because eq.1 accurately predict what happened in the beam. In Figure 8(Experimental value against Load in experiment 1) a linear shape is observed as from Bending moment =Applied Load X Distance (eq. 1) when Applied Load is increasing Bending moment will increase too.

Figure 7: Experimental Bending moment against Theoretical Bending moment.

Figure 8: Experimental Bending moment against Load

Part 2

From table 2 our Experimental value was proved to be agree with the theory as the maximum percentage error between Experimental value and Theoretical value was only 6.6%. From experiment 2 it was proved again that *‘The Bending Moment at the ‘cut’ is equal to the algebraic sum of the moments caused by the forces acting to the left or right of the cut’ as in our experiment the position of the load did effect Bending moment.

Conclusion

The experiment objectives were achieved. By comparing Experimental value to Theoretical value and several graph plotting it was proved to be true that bending moment in a supported beam is equal to applied force times distance, and the bending moment at the ‘cut’ is equal to the sum of moment of force act on right or left of the ‘cut’.

Reference

. Experiments and Statistics, 2014,First year. University of Birmingham.

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