A people-moving conveyor-belt moves a 600-newton person a distance of 100

A people-moving conveyor-belt moves a 600-newton person a distance of 100 meters through the airport.
a. How much work was done?
b. The same 600-newton person lifts his 100-newton carry-on bag upward a distance of 1 meter. They 
travel another 10 meters by riding on the “people mover.” How much work was done in this situation?

2 months ago

Solution 1

Guest Guest #9847817
2 months ago
In a), no work is done to move horizontally 'across" gravity. In b), he does (m) (g) (h) = (100)(9.8)(1) = 980 joules of work to lift the bag, and then no more work is done by the belt to move both of them horizontally.

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    12 inches/1 foot     60 seconds/1 minute     1 meter/100 centimeters

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1 hour = 3,600 seconds  so the fraction is  (3600 sec/hr) .

The unit conversion is:  (1.6 m/s²) x (3600 sec/hr) x (3600 sec/hr)

I multiplied by the fraction twice because we need sec² on top to cancel
the s² on the bottom.

Multiply this out and you get  20,736,000 m/hr². 
Don't let the big number scare you.

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                    Time for the change = (change in speed) / (acceleration)

Change in speed = 30 km/hr

Acceleration was 1.6 m/sec²  but we found that
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And also, since the change in speed is in km,
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                     Time for the change = (30 km/hr) / (20,736 km/hr²)

                     30 / 20,736 = 0.0001447 hour

                                      =  5.2 seconds.

I realize that this has turned into a nightmare.  I probably lost you, and
the answer is likely wrong because the numbers got so ugly.  I apologize. 
The reason for all the ugly numbers is that I apparently picked the wrong
number to change the units.  It probably would have been a lot neater to
convert the change in speed to  m/sec  instead of changing the acceleration
to  m/hr² .  But the principle is the same.  Make a fraction out of the unit you
have and the new unit you want, wit the same value on top and bottom, and
use it to convert the units of one number to match the units of the others.

Change in speed = (30 km/hr) x (1000 m/km) x (1 hr / 3600 sec) = 8.333 m/sec

Time = (change in speed) / (acceleration) = (8.333 m/s) / (1.6 m/s²) = 5.2 seconds

Yes, this way was certainly better and prettier.
But at least I got the same answer going the long tough way!