A 75.0-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 4.30 m. What is the work done on the man by (a) the gravitational force and (b) the escalator?
previous answers were wrong
To find the work done on the man by the gravitational force and the escalator, we need to understand the concept of work and how it is calculated.
Work is defined as the transfer of energy that occurs when a force is applied to an object and the object moves in the direction of the force. Mathematically, work is calculated using the equation:
Work = Force × Distance × cos(θ)
where Force is the magnitude of the force applied to the object, Distance is the distance over which the force is applied, and θ is the angle between the force and the direction of motion.
(a) Work done by the gravitational force:
In this case, the gravitational force is acting vertically downwards. Since the man is moving upward, the angle between the force and the direction of motion is 180 degrees (opposite directions). Therefore, cos(θ) = -1.
Mass of the man, m = 75.0 kg
Gravitational field strength, g = 9.8 m/s² (approximately)
The work done by the gravitational force is given by:
Work_gravity = m × g × h
where h is the vertical height the man is lifted.
Substituting the values:
Work_gravity = 75.0 kg × 9.8 m/s² × 4.30 m
(b) Work done by the escalator:
Since the escalator is moving the man at a constant velocity, the net force acting on the man in the vertical direction is zero. Therefore, the work done by the escalator is zero.
Thus, the work done by the gravitational force is calculated in part (a), while the work done by the escalator is zero.
To find the work done by the gravitational force, multiply the mass of the man by the gravitational field strength (9.8 m/s²) and the height (4.30 m). To find the work done by the escalator, the answer is zero.
a)80
b) 97
1. W(grav) = -mgh
2. W(es) = mgh