AM212 - Rolling on an inclined plane

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Title: Rolling on an inclined plane
Aim: To find the radius of gyration of a body rolling on an inclined plane.
Apparatus:

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THEORY:
*GENERAL KNOWLEDGE*
An inclined plane can be defined as any plane surface positioned at an angle with respect to the horizontal plane. Geometrically, it can also be called right-angled triangle in which, the hypotenuse is the inclined plane, the base is the horizontal plane and the perpendicular is the vertical height. For experimental purposes, the inclined plane consists of two plane parallel plates or surfaces hinged together so that they can be rotated about horizontal axis as the horizontal and inclined planes. The inclined plane is smoothened to minimize the effects of friction and is also provided with a pulley system for different motion related experiments.
Theory 1:
The inclined plane reduces the effect of the force of gravity on an object on the inclined surface by changing the angle of application of the force component.

As per Newton’s second law of motion, Force acting on a body can be described as,

F = Ma  Where F = Vector sum of all the forces (or net resultant force) acting on the object, m = mass of the object and a = acceleration produced in the body due to the effect of forces.



 





Suppose, an object of mass m1 is placed on an inclined plane. It can move upward, downward or remain stationary. In all of these different situations, net force acting on the object will be different. The situations are analyzed using “Free Body Diagrams (FBD)”.

a.)    Without Friction
In diagram 2, consider the object of mass m1 placed on inclined plane. Various forces acting on the object are
(i)   Force of gravity acting vertically downward
(ii)               Tension in the string due to mass m2 suspended from the string connecting the two objects

The free body diagram of the objects under the effect of these forces is as shown in diagram 3. In the diagram,
T = tension in the cord
m1 = mass of the object placed on the inclined plane (i.e., roller)
m2 = mass of the object hanging from the pulley (i.e., weight pan with weights)
N = Normal reaction force due to weight component of the object
q = Angle of inclination
g = Acceleration due to gravity
ax = Acceleration along x-axis
ay = Acceleration along y-axis



b.)    With Friction
In this case, various forces acting on the object are,
(i)            Force of gravity acting vertically downward.
(ii)          Tension in the string due to mass m2 suspended from the string connecting the two objects.
(iii)        Force of friction on the roller.

The free body diagram of the objects under the effect of these forces is as shown in diagram 4.
This case is similar to the previous one except that force of friction between inclined surface and roller is acting on the roller so as to oppose the motion of the roller. The frictional force may be dynamic (acting on the body in motion) or static (acting on the body, when it is stationary and resists the tendency of the body to move from stationary position). The direction of frictional force is opposite to the direction of motion. When the body moves upward on the inclined surface, the frictional force (f) acts in the downward direction, as shown in the diagram 4. If the body is rolling down the inclined surface, frictional force acts in the upward direction.
If, ‘f’ is the force of friction, m is the co-efficient of friction between roller and inclined surface, then
                                                               ………. (5)
In case of static friction, force of static friction (fs, that opposes the movement of a body from the resting position) can be described as

Where, fs is the force applied to just start the motion of body and ms is coefficient of static friction between the two bodies. When the bodies are in motion, let fk be the force required to maintain the uniform speed of motion and mk be coefficient of static friction, then



For Procedures, See your Mechanical Laboratory Manual.

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Observations :-
1.       

Applications:-
PRECAUTIONS:
For Precautions, See General Laboratory Precautions
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About Stephen Djes

Stephen Djes is a passionate Graduate of Engineering from the University of Benin, and he is geared towards helping fellow engineering students in the great institution of UNIBEN to do better at academics.
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