Inclined Plane

Objective:

  1. To find the downward force along an inclined plane, acting on a roller due to the gravitational pull of the earth.
  2. To study its relationship with the angle of inclination θ by plotting a graph between applied force and sin θ.

 

Theory:

              The inclined plane consists of a smooth plane hinged to a base so that it can be set at any desired angle. Consider a heavy metal roller connected to a scale pan by a light extensible string passing over a frictionless pulley resting on the plane as shown in the figure given below.

If a body of mass (say m) is placed over an inclined plane, that is inclined at an angle «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math» with the horizontal, its weight mg acts vertically downward. The component mg cos«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math» of the weight acts normally downward on the plane balances the upward normal reaction (say R) of the inclined plane. The component mg sin«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»  of the weight acting parallel to the inclined plane downwards, produces motion in the body.

If total weight W1=m1g moves the body up and total weight W2 = m2g makes the body move down, 

Then the downward force acting on the body along the inclined plane,

W=\frac{W1+W2}{2}=\frac{\left ( m1+m2 \right )g}{2}  which must be equal to mg sin\Theta

ie; W=mg sinTheta  --------------(1)

For a constant mass,m  W \propto sin \Theta

Thus, a graph between sin θ along X-axis and W along Y-axis must be a straight line.

Learning Outcomes:

  •     Students understand the working of an inclined plane.
  •     Students understand idea of normal reaction and downward force acting on an inclined plane.

 

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