Experiment 1: Equation of Motion: Normal and Tangential I 14007037

LABORATORY REPORT

CVE 3302

ENIGINEERING DYNAMICSBachelor of Civil Engineering

(BCEGI)

Faculty of Science, Technology, Engineering and Mathematics

(FOSTEM)

Name: Fazeen Mohamed

ID: I14007037

Experiment No: 01

Experiment Title: Equation of Motion (Normal and Tangential)

Experiment 1: Equation of Motion: Normal and Tangential I 14007037

Submission Date: 25 – 09 – 2015

Equation of Motion: Normal and Tangential Part A

Equipment Used: Apparatus LS-1234

Objectives

1. Demonstration of the centrifugal motion to prove that it follows the Newton’s LawFn=man.

2. Comparison of experimental results with those calculated from theory.

Procedures

1. Initially the radius of gyration r of both masses was pre-set to be 125 mm from the centre before the experiment.

2. When the masses were positioned properly, the cover door was closed and the main power was switched on.

3. The initial angular speed N was specified by adjusting the speed controller.4. The rotational speed in rpm and the experimental force were recorded down

digitally.5. Step 3 and 4 were repeated to obtain rotational speed.6. The data was recorded in table and graphs of experimental force, Fexp and

theoretical force, Ftheory versus the square of velocity of the mass, v2 were plotted.

Results and Calculations

Radius of gyration, r = 0.125 mMass, m = 0.311 kg (total mass of both rotating masses)

N(rpm)

ω=2πN60

(rad s-1)

v=rω(m s-1)

v2

(m2 s-2)

F exp(N)

F theory=mv2

r(N)

Percentage Error(%)

98 10.26 1.283 1.646 4.0 4.094 2.303153 16.02 2.003 4.011 10.0 9.980 0.205201 21.05 2.631 6.923 18.0 17.22 4.509254 26.60 3.325 11.05 29.0 27.50 1.818302 31.63 3.953 15.65 41.0 38.88 2.881

Experiment 1: Equation of Motion: Normal and Tangential I 14007037

351 36.67 4.595 21.11 56.0 52.52 4.722

0 5 10 15 20 250

10

20

30

40

50

60

ExperimentalTheoretical

Velocity2 (m2S-2)

Forc

e (N

)

Discussions

From the graph plotted (F against V2) using the obtained experimental and theoretical data it is evident that there is a linear relationship between the centrifugal force (experimental and theoretical) and square of the velocity. It is also evident that as velocity increases (thus increases square velocity) the deviation between experimental centrifugal force and theoretical centrifugal force tends to increase.

The cause for these deviation is mainly due to human and mechanical error (machine error) leading to variations. If we look at the formula for calculating centrifugal force theoretically we can identify the components that lead to the human error as well as mechanical error. The formula for calculation of centrifugal force is given as;

F=mv2/r=(mr )v2 If we look at the formula there are three components that might leads to the

error percentage. These include mass, radius and velocity. Error caused by velocity will be minimal as it is set for the experiment at each time, however mass and radius may lead to inaccuracy in the results obtained. Accurate measurements of mass and radius of gyration is required to make the theoretical and experimental force to be equivalent experimentally. The radius was set manually using the scale attached. Hence alignment and adjustment variation may lead to error in the radius set for the

Experiment 1: Equation of Motion: Normal and Tangential I 14007037

experiment. The mass of rotating masses were not calculated, rather given as fixed value which may vary with the actual mass of the objects and may lead to slight variation.

The average error percentage is around 3.23% < 5%, hence the results obtained are acceptable. There is no force acting on the mass when the masses are at rest and force increases as velocity increases.

Conclusions

This experiment signifies that there’s a centrifugal force acting on the object undergoing circular motion at a fixed point. The centrifugal force is perpendicular to the direction of motion so that there’s no acceleration in the direction of motion. Thus this force is required for any object travelling a circular path to complete its rotation about a fixed point. This is also the tangential component of acceleration. It is tangential to the direction of motion of the point. If this component is 0, the motion is uniform circular motion, and the velocity changes in direction only. Since the radius s constant the centrifugal force is directly proportional to the square velocity of the object. Centrifugal force increases as the velocity increases or else the object might deviate from the path. This is because as the rotation speed increases the tangential velocity also increases as shown in this formulaF=mv2/r. This force will help the object to remain in its path. Thus concluding that centrifugal motion follow the Newton’s LawFn=man.

Experiment 1: Equation of Motion: Normal and Tangential I 14007037

Equation of Motion: Normal and Tangential Part B

Equipment Used: Apparatus LS-1234

Objectives

1. Determination of the relationship between centrifugal force, F and the radius of gyration, r.

2. Comparison of experimental results with those calculated from theory.

Procedures

1. Initially the radius of gyration r of both masses was pre-set to be 115 mm from the centre before the experiment.

2. When the masses were positioned properly, the cover door was closed and the main power was switched on.

3. The initial angular speed N was taken as specified 200 rpm by adjusting the speed controller.

4. The experimental force were recorded down digitally.5. Step 1 to 4 were repeated five times with different values of radius of

gyration.6. The data was recorded in table and graphs of experimental force, Fexp and

theoretical force, Ftheory versus the radius of gyration of the mass, r were plotted.

Results and CalculationsN = 200 rpmMass, m = 0.311 kg (total mass of both rotating masses)

F=mr ω2

Where. ω=2πN60

Radius of gyration, r (m) Fexp (N) Ftheory (N) Percentage Error (%)

0.115 16.0 15.69 1.98 %0.125 17.0 17.05 0.293 %0.135 19.0 18.42 3.167 %

Experiment 1: Equation of Motion: Normal and Tangential I 14007037

0.145 20.0 19.78 1.108 %0.155 21.0 21.15 0.686 %0.165 23.0 22.51 2.263 %

0.11 0.12 0.13 0.14 0.15 0.16 0.1715

16

17

18

19

20

21

22

23

24

ExperimentalLinear (Experimental)Theoretical

Radius of gyration, r (m)

Forc

e (N

)

Discussions

The graph is plotted centrifugal force against radius of gyration. Form the graph it is evident that radius of gyration is directly proportional to the centrifugal force. The omega and mass of the object are kept constant in this experiment and

radius is varied to calculate the centrifugal force. There’s variation between the experimental and calculated values and if we consider the formula we can identify

the components that lead to error. The formula for calculating the force is given as F=mr ω2

As of part ‘A’ mass is kept constant, however it is not measured before the experiment, hence slight deviation is possible. The omega is kept constant by keeping the Normal velocity (N) constant. Hence this adjustment is made manually human error is possible and will cause inaccuracy in theoretical and experimental results. Third component is measured radius. Misalignment or adjustment variation might have caused slight deviation in the measured radius. In this experiment also the average error is less than 5%, thus is acceptable.

Experiment 1: Equation of Motion: Normal and Tangential I 14007037

From the calculated results it is significant that for an object with fixed velocity, the centrifugal force increases as the radius of gyration increases. Hence more centrifugal force is required to keep the object in circular path to count for the increase in radius.

Conclusion

A force is required to keep an object moving in circular motion. This force is directly proportional to the radius of gyration with respect to this formula,

F=mr ω2

The experimental results signifies the relationship between centrifugal force and radius of gyration for an object moving in circular motion about a fixed point is directly proportional as the graph is a straight line passing through the origin. The slight deviation in the experimental values is due to human and mechanical error. Hence when radius is increased the centrifugal force also increases to keep the object in circular motion without tripping from its path when angular speed is constant. If radius is zero there will be no centrifugal force acting in the object.

Thus this conclude the relationship between centrifugal force and radius of gyration theoretically and experimentally as directly proportional.