Question

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

Answer 1

a) 3750 J

b) 23.9 W

Step-by-step 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:

`W_1=F_g\Delta h`

where:

`F_g=200 N` is the force applied to lift the suitcase

`\Delta h=10.0 m` is the change in height

Substituting,

`W_1=(200)(10.0)=2000 J`

Work 2) is given by:

`W_2=Fd`

where

F = 50.0 N is the horizontal force

d = 35.0 m is the displacement

Substituting,

`W_2=(50.0)(35.0)=1750 J`

So, the total work done by Ben is

`W=W_1+W_2=2000+1750=3750 J`

b)

The power consumed is given by:

`P=(W)/(t)`

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:

`t_1 = 1.45 min \cdot 60 = 87 s`

The time elapsed when pushing the suitcase horizontally is

`t_2 = (d)/(v)=(35.0 m)/(0.5 m/s)=70 s`

So the total time is

`t=t_1+t_2=87+70=157 s`

And so, the power is:

`P=(3750)/(157)=23.9 W`