Faculty Of Engineering And Information TechnologyMEE 3219 Engineering Dynamics

Lab ReportExperiment 2: Equation of Motion Normal and Tangential

Name : Ehsan Samoh Program : BMEGI ID : I14005275Date of experiment conducted : 28th of Jan 2015

Part A: Experiment Equation of Motion: Normal and Tangential

1. Introduction

The first law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant.The first law can be stated mathematically as

Consequently, An object that is at rest will stay at rest unless an external force acts upon it. An object that is in motion will not change its velocity unless an external force acts upon it.This is known as uniform motion. An object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest. If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continually move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely.

Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speed. Newton's first law is often referred to as the law of inertia. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero.In every material universe, the motion of a particle in a preferential reference frame is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in . That is, a particle initially at rest or in uniform motion in the preferential frame continues in that state unless compelled by forces to change it.Newton's laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity.

2. Procedure and Apparatus

Equipment: Compound Pendulum apparatus LS-1232, stopwatch

Procedure:1.A pre-installed mass is applied onto the apparatus to carry out on the experiment of centrifugal force.

2.Preset the radius of gyration, r. (e.g: 125mm from the center) before starting the experiment. Note: the radius of gyration, r for both mass must be equal to stabilize the centrifugal force apparatus.

3.Switch on the main power supply when the mass have been positioned properly.

4.Make sure that the cover door is closed before proceeding to the next step.

5. Next specified the angular speed, N, (e.g.: 50 rpm) by adjusting the speed controller and record down the rotational speed, rpm from the digital meter provided.

6. Repeat step 4 and 5 by changing the rotational speed, up to maximum of 500 rpm.

7. Record the data obtained in Table 1.1 and plot the graphs experimental force, Fexp, and theoretical force, Ftheory versus the square velocity of the mass, v2.

3. Data and discussion

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

experimentN(rpm)(rad/s)

v = r

(m/s)v2Fexperimental

(N)Ftheoretical

(N)% error

160

6.280.7850.6111.5334.6

212012.561.562.4666.121.96

318018.842.355.541413.72.18

424025.133.149.862624.535.99

530031.413.9215.44138.317.02

636037.694.7122.185955.186.92

Table 3.1The result obtain from the experiment is plotted in table 3.1

Ftheoretical = The following formulas were used:

v = r

Ftheory

% error=(F exp-F theory)/F theory

Based on the theoretical values obtained, using the formula, the following graph was obtained by comparing the experimental and theoretical values of the centrifugal force (F).

Figure 3.2According to the graph plotted in figure 3.2, Force is directly proportional to velocity square. There is a slight difference between the F exp and F theory. This is caused by human error. Overall the graph is obey the theory.

4. Conclusion The experiment conducted demonstrated that centrifugal motion follows Newtons Law. It is seen from the graph that as the velocity increases, the force increases as well.This can be verified by comparing the experimental and theoretical data. It is seen that the variation in the results is very less which gives a very less experimental error. This may be due to factors such as the apparatus being old. Hence the experiment was successful.

5. Reference

1. Newton law of motion available athttp://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

Part B: Experiment Equation of Motion: Normal and Tangential

1.1 IntroductionThe magnitude of the centripetal force on an object of mass m moving at tangential speed v along a path with radius of curvature r is

where a c is the centripetal acceleration. The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle, the circle that best fits the local path of the object, if the path is not circular. The speed in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. This force is also sometimes written in terms of the angular velocity of the object about the center of the circle:

The objective of this experiment is to determine the relationship between centrifugal force, F and the radius of gyration, r.

1.2.2 Apparatus and procedure

Equipment: Apparatus LS-1234

Procedure:

1.A pre-installed mass is applied onto the apparatus to carry out on the experiment of centrifugal force.

2.Preset the radius of gyration, r. (e.g.: 125mm from the center) before starting the experiment. Note: the radius of gyration, r for both mass must be equal to stabilize the centrifugal force apparatus.

3.Switch on the main power supply when the mass have been positioned properly.

4.Make sure that the cover door is closed before proceeding to the next step.

5.Next fix the rotational speed to a constant value along the experiment (eg: 200 rpm) by adjusting the speed controller.

6.Record down the value of the centrifugal force from the digital meter.

7.Repeat step 2 to 4 with different values of radius gyration, r.

8. Record the data obtained in Table 1.2 and plot the graphs of experimental force, Fexp, and theoretical force, Ftheory versus the radius of gyration, r.

1.2.3 Data and discussion

N = 200 rpmMass m = 0.311 kg (total mass of both rotating masses)Radius of gyration, r(m)Fexperimental

(N)Ftheoretical

(N)% error

0.1151614.3111.80

0.1251815.6814.79

0.1351917.0411.50

0.1452018.408.69

0.1552119.776.22

0.1652221.134.11

Table 1.2.3.1The result obtain from the experiment is plotted in table 1.2.3.1

The following formulas were used to calculate the theoretical results of the centrifugal force F.

v = r

Ftheory

% error=(F exp-F theory)/F theory

Based on the experimental and theoretical values of centrifugal force calculated, a graph of Force vs radius of gyration, r was plotted.

Figure 1.2.3.2According to the graph plotted in figure 1.2.3.2, Force is directly proportional to velocity square. There is a slight difference between the F exp and F theory. This is caused by human error. Overall the graph is obey the theory.

1.2.4 ConclusionThe experiment was successful in determining the relationship between the centrifugal force and radius of gyration. It is seen from the graph that as radius increases, the force increases as well. This gives a linear relationship. The experimental and theoretical values were compared which showed only a slight difference. This may be due to the wearing off of the apparatus and human error of recording the values by rounding off and not the exact values. However a low percentage error concludes that the experiment conducted was successful.

1.2.5 Reference

1. Centripetal force available athttp://en.wikipedia.org/wiki/Centripetal_force