23 A block of mass m is placed at relative equilibrium on an inclined ...
Analysis:
To find the instantaneous power supplied by friction to the block, we need to consider the forces acting on the block and determine the work done by friction.
Forces acting on the block:
1. Weight: The weight of the block acts vertically downwards and can be calculated as W = mg, where m is the mass of the block and g is the acceleration due to gravity.
2. Normal force: The normal force acts perpendicular to the inclined plane and counteracts the component of the weight that is perpendicular to the plane. It can be calculated as N = mgcosθ, where θ is the angle of inclination.
3. Friction force: The friction force acts parallel to the inclined plane and opposes the motion of the block. It can be calculated as F = μN, where μ is the coefficient of friction.
Work done by friction:
The work done by friction can be calculated as the product of the friction force and the displacement of the block along the inclined plane. Since the block is in relative equilibrium, the net force acting on it along the inclined plane is zero. Therefore, the work done by friction is given by Wf = Fd, where d is the displacement of the block.
Instantaneous power supplied by friction:
Power is defined as the rate at which work is done. Therefore, the instantaneous power supplied by friction can be calculated as P = Wf/t, where t is the time taken to do the work.
Calculating the displacement:
The displacement of the block along the inclined plane can be calculated using the formula d = Vot, where Vo is the constant velocity of the lift and t is the time taken.
Calculating the time taken:
Since the block is in relative equilibrium, the lift is moving upwards with a constant velocity. This means that the net force acting on the block along the inclined plane is zero. Therefore, the acceleration of the block along the inclined plane is zero. Using the equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken, we can substitute v = 0 and a = 0 to get t = (0 - Vo)/0 = 0. Therefore, the time taken is zero.
Calculating the power:
Since the time taken is zero, the instantaneous power supplied by friction is P = Wf/0 = undefined.
Conclusion:
The instantaneous power supplied by friction to the block is undefined because the time taken is zero. This means that no work is being done by friction on the block.
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