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

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:

$P=\frac{W}{t}$

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

$t_2 = \frac{d}{v}=\frac{35.0 m}{0.5 m/s}=70 s$

So the total time is

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

And so, the power is:

$P=\frac{3750}{157}=23.9 W$