Question

A man pushes on piano with mass 170 kg; it slides at constant velocity down a ramp that is inclined at 20.0 ∘ above the horizontal floor. Neglect any friction acting on the piano.

Answer 1

To calculate the work done by the man, we need to first calculate the net force acting on the crate. We can determine the net force by resolving the force applied by the man into its components. The component of the force parallel to the ramp will move the crate up the ramp, while the component perpendicular to the ramp will cancel out due to the normal force.

Step-by-step explanation:

To calculate the work done by the man, we need to first calculate the net force acting on the crate. We can determine the net force by resolving the force applied by the man into its components. The component of the force parallel to the ramp will move the crate up the ramp, while the component perpendicular to the ramp will cancel out due to the normal force.

To calculate the work done on the crate, we can use the formula:

Work = Force * Distance * cos(angle)

where the angle is the angle between the force and the direction of displacement. Substituting the given values, we find:

Work = 500 N * 4.00 m * cos(20.0°)

Next, we need to calculate the work done on the man himself as he moves up the ramp. Since he moves at a constant speed, the net work done on him will be zero. This means that the work done on the crate will be equal in magnitude but opposite in direction to the work done on the man. Therefore, the total work done by the man is:

Work = - Work on crate = - (500 N * 4.00 m * cos(20.0°))

Answer 2

given,

mass of the piano = 170 kg

angle of the inclination = 20°

moves with constant velocity hence acceleration = 0 m/s²

neglecting friction

so, force required to pull the piano

F = m g sin θ

F = 170 × 9.81 × sin 20°

F = 570.39 N

so, force required by the man to push the piano is F = 570.39 N