Calculating Work Done on Karen by Woodley Park Station Escalator

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SUMMARY

The discussion focuses on calculating the work done by an escalator on Karen, who has a mass of 54 kg, as she rides the longest escalator in the world at Woodley Park Station. The work is calculated using the formula W=F*x*cos(theta), where the force exerted by the escalator is determined to be 259.786 N. The total work done is computed as 15,457.28 J, assuming the angle between the force and displacement is 0 degrees. The calculation is confirmed to be accurate, with a note on the importance of using precise values in trigonometric functions.

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Homework Statement


Karen has a mass of 54 kg as she rides the
up escalator at Woodley Park Station of the
Washington D.C. Metro. Karen rode a dis-
tance of 59:5 m, the longest escalator in the
free world.
The acceleration of gravity is 9:8 m=s2 :
How much work did the escalator do on
Karen if it has an inclination of 29:4±? Answer
in units of J.


Homework Equations


W=F*x*cos(theta)
where F= force, x is displacement and theta is the angle between the 2


The Attempt at a Solution


I first drew a force diagram. And used it to figure out this:
mg=529.2N
F=529.2*cos60.6=259.786N <-force of escalator
Next i plugged it into the Work equation:
the angle between the displacement and force is 0, so cos(theta)=1:
W=259.786*59.5*1=15457.28285J

is this right? I just need a confirmation, because I can't afford to get this wrong. Ty in advance
 
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looks good!
 
but using 60 instead of the exact value makes your answer inaccurate
 
60? for:
F=529.2*cos60.6=259.786N <-force of escalator
 
haha, sorry, I didn't see the .6
 

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