Final answer:
To calculate the work done by a person climbing a downward-moving escalator, use the formula W = mgh, which represents the gravitational work based on the vertical height gained. The escalator's motion affects the rate of climb but not the total gravitational work, which depends only on vertical displacement. Additional kinetic energy would be included if there's a change in horizontal velocity.
Step-by-step explanation:
To calculate the work done by someone climbing up a downward-moving escalator, you start by considering the work done against gravity. This work is given by the formula W = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s² on Earth), and h is the vertical height gained.
When the escalator is moving downward, the person must work not only against gravity but also against the motion of the escalator to reach the top.
If the person is climbing at 1.5 times the speed of the escalator, then their overall speed relative to the ground is their climbing speed plus the escalator's speed. The work done by the person then takes into account the total vertical distance traversed against gravity in a given time.
The movement of the escalator does not change the total gravitational work done because gravity acts only on the vertical displacement, regardless of the horizontal component of motion.
The total work done is the sum of the gravitational work and any additional kinetic energy imparted to the climber, calculated as W = KE + PE, where KE represents the kinetic energy if there is any change in the horizontal velocity, and PE represents the gravitational potential energy (mgh).