When a mass is being pushed with a force F down an inclined plane with uniform speed, the force that does the maximum work is the applied force F. Let's analyze the forces involved and their effects on the work done:
Applied Force (F): This is the force exerted on the object to move it down the inclined plane. When the object moves with uniform speed, the applied force is equal in magnitude but opposite in direction to the force of friction. The work done by the applied force is calculated as W = F * d * cos(theta), where d is the distance moved and theta is the angle between the applied force and the direction of motion. Since the cosine of 0 degrees is 1, the work done by the applied force is maximized.
Frictional Force: The force of friction acts in the opposite direction to the applied force and is necessary to maintain the uniform speed of the object. The work done by friction is given by W = f * d * cos(theta), where f is the magnitude of the frictional force. However, the work done by friction is negative since it opposes the motion of the object. Friction does negative work because the displacement and the force of friction are in opposite directions.
Weight of the Body: The weight of the body acts vertically downward due to gravity and is perpendicular to the direction of motion on the inclined plane. Since the weight is perpendicular to the displacement, the work done by the weight is zero (W = F * d * cos(theta) = F * d * cos(90 degrees) = 0).
Normal Reaction: The normal reaction is the force exerted by the inclined plane on the object perpendicular to the plane's surface. It does not contribute to the work done since it acts at 90 degrees to the direction of motion. Therefore, the work done by the normal reaction is also zero.
In conclusion, the applied force F does the maximum positive work, while the frictional force does negative work to balance it out. The weight of the body and the normal reaction do no work in this scenario.