Ben Travlun carries a 200-N suitcase up three flights of stairs (a height of 10.0 m) in 1.45 minutes and then pushes it with a horizontal force of 50.0 N at a constant speed of 0.5 m/s for a horizontal distance of 35.0 meters. How much work does Ben do on his suitcase during this entire motion? And how much power does Ben consume in this entire motion

a) 3750 J

b) 23.9 W

Explanation:

a)

The work done by Ben consists of two parts:

1- The work done by lifting the suitcase

2- The work done by pushing the suitcase horizontally

Work 1) is given by:

where:

is the force applied to lift the suitcase

is the change in height

Substituting,

Work 2) is given by:

where

F = 50.0 N is the horizontal force

d = 35.0 m is the displacement

Substituting,

So, the total work done by Ben is

b)

The power consumed is given by:

where

W is the work done

t is the time elapsed

In this problem:

W = 3750 J is the work done by Ben

The time elapsed for lifting the suitcase is:

The time elapsed when pushing the suitcase horizontally is

So the total time is

And so, the power is:

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