You stand on a bathroom scale inside an elevator, press the button to go up and

Question

You stand on a bathroom scale inside an elevator, press the button to go up and watch your weight change. Suppose during the first 5 seconds your apparent weight is 165 lbs, then for 5 seconds your apparent weight is equal to your true weight of 160 lbs, finally, for the last 5 seconds your apparent weight is 155 lbs. Full points will be awarded for the correct answer to the following question: By what amount did the gravitational potential energy of your body change over these 30 seconds? _____ If the full credit cannot be awarded, then partial credit will be awarded for the correct answers to the following questions: i) What Is your true weight in SI units? ____ ii) What was the direction of your acceleration during the first 10-second interval? _____ iii) What was the magnitude of your acceleration during the first 10-s interval? _____ iv) What distance did you travel during that first 10-s interval? Up or down? ____ v) How fast were you traveling by the end of that first 10-s interval? _____ vi) How far do you travel during the second 10-s interval? _____ vii) What is the magnitude of your acceleration during the last (3rd) 10-s interval? ____ viii) What is the direction of your acceleration during the last (3rd) 10-s interval? _____ ix) What distance do you travel during that last 10-s interval? Up or down? _____ x) Adding the total distance traveled, what is the change in your gravitational potential energy? ____

Explanation / Answer

i)

true weight W1 = 160 lb = 160*4.45 = 712 N

ii)

along +y axis

iii)

during first 5 seconds

apparent weight w2 = 165 lbs = 165*4.45 = 734.25 N

W2 - W1 = m*a

734.25 - 712 = (712/9.8)*a

acceleration a1 = 0.306 m/s^2

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iv)

y1 = vo*t1 + (1/2)*a1*t1^2

y1 = 0 + (1/2)*0.306*5^2 = 3.825 m up

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v)

v1 = vo + a1*t1 = 0 + 0.306*5 = 1.53 m/s

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vi)

t2 = 5 s

herea acceleration a2 = 0

y2 = v1*t = 1.53*5 = 7.65 m

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vii)

W3 - W1 = -m*a3

734.25 - 712 = -(712/9.8)*a

acceleration a1 = -0.306 m/s^2

magnitude a3 = 0.306 m/s^2

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viii)

down wards -y axis
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xi)

y3 = v1*t3 + (1/2)*a3*t3^2

y3 = (1.53*5) - (1/2)*0.306*5^2

y3 = 3.825 m

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x)

total distance y = y1 + y2 + y3 = 3.825 + 7.65 + 3.825 = 15.3 m

change in potential energy dU = W1*h = 71.2*15.3 = 1089.36 N

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