Introduction
This experiment was conducted with the knowledge of the fact that centripetal force changes with the change in the angular velocity, the mass of the body in circular motion, and the radius of the circular path. The aim of the experiment include;
To discover and quantify the factors that determine the force required to keep an object in uniform circular motion
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To use graphical analysis to derive/verify the equation for centripetal force
To investigate the behaviour of friction in a circular motion.
At the end of the experiment, graphs of force against mass and force against angular velocity are expected to be linear with a positive gradient. Impliedly, the centripetal force increases with an increase in the other variables. Conversely, a graph of force against a radius is a straight line with a negative gradient.
Background
A body moving in a circular motion experiences a change in its linear velocity. Since the path of motion is a circle, its linear velocity can be determined at various points of the circular path and it is known as the tangential velocity. In addition, for a body to remain in circular motion, then there are various factors that should be considered. One of them is the magnitude of the angular velocity. Notably, the higher the angular velocity, the higher the amount of force required to keep this body in uniform circular motion. Secondly, this value depends on the mass of the body in circulation. Importantly, the magnitude of the centripetal force required increases with the increase in the mass of the object moving in circular motion. Lastly, the force depends on the radius of the circular path. It is worth noting that the shorter the radius, the higher the amount of force required to keep a body in the motion described above.
Methodology
This experiment was conducted to determine the amount of force that acts on a body in uniform circular motion. Some of the apparatus used in the experiment include the virtual centripetal force lab, a graph, and a pencil. The data was recorded in an excel file and a graph drawn. The speed of the turntable was adjusted to between 15 and 20 rpm. The vector display was turned on and off using the toggle switch. The procedure was repeated with various values of the angular velocity and the corresponding values of the tangential velocity recorded. Next, the masses of the rolling cylinder was adjusted and the values of the corresponding centripetal force recorded. Lastly, the radius of the circular path was recorded and a graph of force against radius plotted. These graphs were used to verify the formula of uniform circular motion.
Data
| trial | mass | force |
|
1 |
5 |
5.975 |
|
2 |
10 |
11.95 |
|
3 |
15 |
17.925 |
|
4 |
20 |
23.09 |
|
5 |
25 |
29.875 |
|
6 |
30 |
35.85 |
|
7 |
35 |
41.825 |
|
8 |
40 |
47.8 |
|
9 |
45 |
53.775 |
|
10 |
50 |
59.75 |
Analysis
From the graph, it can be noted that the amount of centripetal force increases with an increase in the mass of the body in uniform circular motion. Thus, the gradient of the graph is positive because it rises to the right. The gradient gives the centripetal force of the mass placed on the turntable. When there is no mass on the turntable, it means there is no centripetal force.
From F= (mv 2 )/r, it can be seen that centripetal force increases with an increase in the mass of an object because the two variables are directly proportional.
Conclusions
The lab experiment above has helped in the understanding of the behaviour of centripetal force based on changes in various factors such as mass, angular velocity, and radius of the circular path. In such a way, the formula F= (mv 2 )/r has been verified.
