A 86.0-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 5.50 m. What is the work done on the man by each of the following forces?
work is defined to be force times displacement
To find the work done on the man by each force, we need to consider the definition of work. Work is defined as the product of force and displacement in the direction of the force.
In this scenario, there are two forces acting on the man: the force of gravity and the force exerted by the escalator. Let's calculate the work done by each force separately:
1. Work done by the force of gravity:
The force of gravity is given by the formula F = mg, where m is the mass of the man and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the force of gravity acting on the man is F_gravity = mg.
The displacement is the vertical height the man moves, which is given as 5.50 m.
Therefore, the work done by the force of gravity is W_gravity = F_gravity * displacement = mg * displacement.
2. Work done by the escalator:
The escalator moves the man at a constant velocity, which means there is no net force applied by the escalator in the vertical direction. Therefore, the work done by the escalator is zero (W_escalator = 0).
Now we can substitute the given values into the equations to find the work done by each force:
1. Work done by the force of gravity:
W_gravity = mg * displacement
W_gravity = 86.0 kg * 9.8 m/s^2 * 5.50 m
2. Work done by the escalator:
W_escalator = 0
Calculating these values will give you the work done by each force on the man.