A 58.0-kg man is riding an escalator in a shopping mall. The escalator moves the man at a constant velocity from ground level to the floor above, a vertical height of 3.70 m. What is the work done on the man by (a) the gravitational force and (b) the escalator?

change in potential energy = m g h

the gravitation force is opposite to the direction of motion so work done = -m g h
the escalator force is in the direction of motion so work done by it is +m g h

58.0*9.8*3.70

=-2100 j 3 sig fig

b) 2100 j 3 sig fig

thanks Damon

To find the work done on the man by the gravitational force and the escalator, we first need to understand the concept of work.

Work is defined as the product of force and displacement in the direction of the force. In this case, the gravitational force and the vertical displacement are involved.

(a) Work done by the gravitational force:
The work done by the gravitational force can be calculated using the formula:

Work = Force × Displacement × cos(θ)

Where:
Force is the gravitational force acting on the man, which is equal to his weight: Force = mass × acceleration due to gravity.
Displacement is the vertical distance covered by the man, which is 3.70 m.
θ is the angle between the force and the direction of displacement. In this case, the force and displacement are in the same vertical direction, so θ = 0°.

Substituting the values, we have:
Work = (mass × acceleration due to gravity) × 3.70 × cos(0°)

The mass of the man is given as 58.0 kg, and the acceleration due to gravity is approximately 9.8 m/s².

Calculating, we get:
Work = (58.0 kg × 9.8 m/s²) × 3.70 × cos(0°)

(b) Work done by the escalator:
Since the escalator is moving the man at a constant velocity, no net force is being applied in the vertical direction. Therefore, the work done by the escalator is zero.

So, in this case:
(a) The work done on the man by the gravitational force is given by the formula:
Work = (mass × acceleration due to gravity) × 3.70 × cos(0°)

(b) The work done on the man by the escalator is zero.

Calculating the values using the appropriate formulas will give you the numerical answers.