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 5.00 m. What is the work done on the man by (a) the gravitational force and (b) the escalator

Answer

a) - 2842 J

b) 2842 J

Explanation:

The escalator is moving the man of mass 58 kg till the height of 5 meters

So here;

m=58 kg

distance = height = h = 5 m

gravitational acceleration = g = 9.8 m/sec2

a) We know work is scalar product of force and displacement

i-e Work = F. S = FS cosθ, where θ is the angle between force vector and displacement vector

When escalator is moving up - the gravitational force is acting downward i - opposite to displcacement i-e angle between force and displacement is 180 degrees.

we have data

m = 58 kg

F=mg = 58*9.8=568.4 N

S=5 m

Work = F. S=FS cos 180°=568.4*5 * (-1) = - 2842 J

So the work done by gravitational force is - 2842 J and - ve sign here indicates that distance is traveled in opposite direction of force.

b) When escalator is moving up the, force is exerted by the escalator equal to gravitational force and the displacement is in the same direction so the angle between force and displacement is 0 degrees

Work = F. S=FS cos (0) = 568.4*5*1=2842 J

So work done by the gravitational force then will be 2842 J

So in both cases work is same but in opposite directions.