An escalator in a shopping centre carries people up through a height h at a vertical speed of
v, but you’re in a hurry when you step onto it, so you climb the moving steps (each with a
height of h
) at a rate of n steps/s. Determine:
4.1 the amount of chemical energy converted into mechanical energy by your leg muscles
s
during your escalator ride, given that your mass is m;
4.2 the work the escalator motor does on you;
4.3The total amount of work done by your legs and the escalator in getting you to the top.
Are you perhaps trying the find the answer to this week's weekly problem set? I think I need to give you a stern talking to.
To determine the answers, we need to consider the following:
1. The energy converted by your leg muscles:
When you climb the moving steps of the escalator, you are exerting force against gravity to move upward. This requires energy from your leg muscles. The amount of energy expended can be calculated using the formula:
Energy = force × distance
The force required is equal to your weight, which is given by the equation:
Force = mass × acceleration due to gravity
The distance is the height h that you climb.
Therefore, the energy converted by your leg muscles is:
ΔE = (mass × gravity) × height
where mass is m (given) and gravity is approximately 9.8 m/s².
2. The work done by the escalator motor on you:
While climbing the moving steps, the escalator is also carrying you up with a vertical speed v. The power output of the escalator motor is equal to the work done per unit time. The work done is given by:
Work = force × distance
The force applied by the escalator motor is the force required to carry your weight and the distance is the height h.
Therefore, the work done by the escalator motor is:
Work = (mass × gravity) × height
3. The total work done by your legs and the escalator:
The total work done is the sum of the work done by your legs and the escalator. It can be calculated by adding the work done by your leg muscles (ΔE) and the work done by the escalator motor.
Therefore, the total work done is:
Total work = ΔE + Work
Let's use these formulas to calculate the answers to your questions. Please provide the values for mass (m), height (h), vertical speed (v), and the number of steps per second (n) so that we can proceed with the calculations.