Question

The stair stepper is a novel exercise machine that attempts to reproduce the work done against gravity by walking up stairs. With each step, Brad (of mass 60 kg) simulates stepping up a vertical distance of 0.25 m with this machine. If Brad exercises for 20 min per day with a stair stepper at a frequency of 60 steps per minute, what total work he does he do each day? The acceleration of gravity is 9.8 m/s 2 .

Answer 1

The total work done by Brad each day is 176400 J

Step-by-step explanation:

Hi there! The work done by a force (F) pointed in the same direction as the displacement (d) is calculated as follows:

W = F · d

The force applied is equal to the weight of Brad, that is calculated as follows:

Weight = m · g

Where:

m = mass of Brad

g = acceleration due to gravity (9.8 m/s²)

Then:

Weight = 60 kg · 9.8 m/s² = 588 N

Let´s find the vertical distance traveled by Brad each day:

He exercises 20 min per day. Each minute Brad does 60 steps. In total, Brad steps up (20 min · 60 steps/min) 1200 steps. If each step has a height of 0.25 m, the total distance traveled by Brad will be

(1200 steps · 0.25 m/step) 300 m.

Then, the total work done by Brad is

W = F · d

W = 588 N · 300 m

W = 176400 J

The total work done by Brad each day is 176400 J