University of Birmingham
Mechanical Engineering
Experiments and Statistics
The Short Laboratory Report
AM1.2A: Centrifugal Force
Submitted by: Stelio Michael Machado Antonas (Student number: 1315848)
Group 2
Date of submission: 08/04/2014
1. Introduction
An object moving with a non-constant speed in a straight line is undergoing acceleration. If an object moves with a constant speed but with non-constant direction, it is also undergoing acceleration. Both types of accelerations is caused by a force. Change in the direction of an object is called centrifugal acceleration, and the force producing the centrifugal acceleration is called centrifugal force. This report will talk about the centrifugal force and its relation with mass, speed and radius. The report is divided into four main sections. It will first consider the theory behind the calculations and how the experiment was conducted. It will then show different results that were taken in the experiment. It will then go on to show and explain the results obtained. Finally some conclusion will be provided as to explain the errors and difference between the theoretical and experimental result.
2. Objectives
The purpose of this experiment is to determine the relationship between the centrifugal force and: 1. the square of the angular velocity, 2. the mass and 3. the radius of orbit for a body that is undergoing centrifugal acceleration
3. Theory
For circular motion to occur there must be a constant force acting on a body, pushing it toward the centre of the circular path. This force is the centripetal force. The magnitude of the centripetal force is directly proportional the mass m of the body, its angular velocity squared and the radius of its path, as shown in equation 1. Since for every action there is an equal reaction, according to Newton's third law of motion, the centripetal force is balanced by a reaction force that is the centrifugal force. The two forces have the same magnitude but opposite direction.
F=mω2r=mv2r (Equation 1)
3.1. Apparatus
The device that was used in the experiment is a TM1005 for experiments in centrifugal force and angular velocity. The mechanism has three balance arms. Two arms in the outside hold any of the selected masses at any of five radial positions. A sensor measures the centrifugal force due to the selected mass as it rotates about the given radii. The other arm holds equal masses in an equal and opposite radius to balance the first mass. This prevents unnecessary vibrations, which would affect measurement accuracy. The motor works in clockwise and anticlockwise rotation and with variable velocity
Figure 1: TM1005 for experiments in centrifugal force and angular velocity.
4. Procedure
Before each experiment, the reading from the force has to be adjusted to zero. The first experiment was to measure the centrifugal force with a fixed mass of 0.1 kg and radius of 0.1 m but with a varied speed. Weights of 0.1 kg were first put onto the arms in the radial position of 0.1 m and then the velocity was adjusted to 5 rad/s and the reading of the centrifugal force was taken. For every increasing of 5 rad/s in the velocity, readings of the centrifugal force were taken. A total of 6 different velocity were recorder.
The second experiment was to measure the centrifugal force with a fixed speed of 30 rad/s and radius of 0.1 m but with varied mass. Weights of 0.02 kg were first put onto the arms in the radial position of 0.1 m and then the velocity was adjusted to 30 rad/s and the reading of the centrifugal force was taken. For every increasing of 0.02 kg onto the arms readings of the centrifugal force were taken until the last mass of 0.1 kg.
The third and final experiment was measure the centrifugal force with a fixed speed of 30 rad/s and mass of 0.1 kg but with varied radius. Weights of 0.1 kg were first put onto the arms in the radial position of 0.02 m and then the velocity was adjusted to 30 rad/s and the reading of the centrifugal force was taken. For every increasing of 0.02 m of radius along the arm, readings of the centrifugal force were taken. A total of 5 different position were recorder
5. Data obtained
Table 1: Results of fixed mass and radius, varied speed.
Radius (r) = 0.1 m; Total mass of matching weights (m) = 0.1 kg
ω(rad/s)
ω2
rω2
Theoretical Force F (N)
Actual Force F (N)
0
0
0
0
0
5
25
2.5
0.25
0.25
10
100
10
1
1.01
15
225
22.5
2.25
2.25
20
400
40
4
4.01
25
625
62.5
6.25
6.27
30
900
90
9
9.03
Table 2: Results of fixed speed and radius, varied mass.
Radius (r) = 0.1 m; Speed (ω) = 30 rad/s; rω2= 90
Total Mass (g)
Mass m (kg)
Theoretical Force F (N)
Actual Force F (N)
0
0
0
0
20
0.02
1.8
1.83
40
0.04
3.6
3.61
60
0.06
5.4
5.42
80
0.08
7.2
7.19
100
0.10
9
8.96
Table 3: Results of fixed speed and mass, varied radius.
Speed (ω) = 30 rad/s; Total mass of matching weights (m) kg = 0.1
Radius (r) m
rω2
Theoretical Force F (N)
Actual Force F (N)
0
0
0
0
0.02
18
1.8
1.78
0.04
36
3.6
3.55
0.06
54
5.4
5.34
0.08
72
7.2
7.18
0.1
90
9
8.94
6. Observation and results
In the first experiment, since the radius and the mass are constant the centrifugal force increases as the angular velocity increases, as shown in figure 2, since the centrifugal force is directly proportional to the angular velocity. In the second experiment, the centrifugal force also increases but this time it increases as the mass increases, as shown in figure 3, since the angular velocity and the radius are constant and the centrifugal force is directly proportional to the mass as shown in equation 1. In the last experiment the centrifugal force increases with the radius increment, as shown in figure 4, since the angular velocity and the mass are constant and the centrifugal force is directly proportional to the radius as shown in equation 1.
Figure 2: Relation between centrifugal force and the angular velocity squared.
Figure 3: Relation between centrifugal force and mass
Figure 4: Relation between centrifugal force and the radius.
7. Discussion
From the result obtained it can be noticed that the relation between the centrifugal force, mass, angular velocity and radius is linear. If the mass, speed or radius changes, the centrifugal force will change since the centrifugal force is a consequence of inertia, the masses tend to continue travel in a straight line and this cause the centrifugal force, so as bigger the speed, the mass or the position of the mass the bigger will be the centrifugal force.
8. Conclusion
From the experiment carried out in centrifugal force in can be concluded that changing the variables in our experiment affected the results greatly. The increase of the angular velocity, mass or radius made the centripetal force go up. The theoretical and experimental results are almost the same with a small difference between them caused by some error that took place during the experiment conducted. It was difficult to set up the angular velocity exactly right, there were some difference in decimals that could cause the changing in the readings. The machine couldn't have been calibrated that give non-accurate readings. In order to overcome these error and to get the accurate value of the experiment, things need to be put into consideration. Firstly, the person doing the experiment need to wait until the machine reaches stable conditions, and carefully set up the speed exactly right and before the experiment is conducted the machine used must be ensure to be functioning well.
Centrifugal force vs radius
Raduis (m)
Centrifugal force (N)
Centrifugal force vs Mass
Mass (kg)
Force (N)
Centrifugal force vs ²
² (rad/s)
Centrifugal force (N)
