you stand on a bathroom scale inside an elevator press the button to go up and w

Question

you stand on a bathroom scale inside an elevator press the button to go up and wach your weight change. Suppose durig the first 10sec your apparent weight is 165lbs, then for 10 secs your apparent waight is equal to your true weight of 160lbs, finally, for the last 10 secs your apparent weight is 155lbs.

1.By what amount did the gravitational potential energy of your body change over these 30secs?

2.what is your true weight in si units

3.what was the direction of your acceleration during the first 10 sec interval?

4.what was the magnitude of your acceleration during th first 10-s intervals?

5.what distance did you travel during that first 10-s? Up or down?

6.how fast were you traveling by the end of that first 10-s interval?

7.how far do you travel during the 2nd 10-s interval?

8.what is the mgnitude of your acceleration during that last (3rd) 10sec interval

9.what is the direction of your acceleration during that last 3rd 10-s interval?

10. what distance do travel during that last 10-s interval?up or down?

11. Adding the total distance traveled, what is that change in your gravitational potential energy?

ay what amount What true weightin units was he direction of your acceleration during the rest o secondintervan What was the magnitude of your acceleration during the first 10 s interval? What distance did you travel during that first 1osinterval upor down? v) How fast were you traveling by the end of that first 10 sinterva7 vi How far do you travel during the second 10-s interval vi) What is the magnitude of your acceleration during thelast(3rd) 10 sinterval? viii) What is the direction of your acceleration during the last (3rd) 10-s interval? What distance do you travel during that last 10-s interval? Up or down? Adding the total distance traveled, what is the change in your gravitational potential energy?

Explanation / Answer

m = mass = actual weight /g = 160 lbs/g = 72.6 kg

while the elevator goes up

Fn = apparent weight = 165 lbs = 74.84 x 9.8 = 733.43 N

using the equation

Fn - mg = ma

733.43 - 72.6 x 9.8 = 7.41 a

a = 2.96 m/s2

Vo = initial velocity = 0

t = 10 sec

using the equation

h1 = Vo t + (0.5) at2

h1 = (0) (10) + (0.5) (2.96) (10)2

h1 = 148 m

Vf = final velocity at the end of 10 sec

Vf = Vo + at = 0 + (2.96) (10) = 29.6 m/s

10 - 20 second period :

since apparent weight = actual weight

hence a = 0

h2 = Vf t

h2 = 29.6 x 10 = 296 m

For last 10 sec :

while the elevator goes up

Fn = apparent weight = 155 lbs = 70.31 x 9.8 = 689.04 N

using the equation

Fn - mg = ma

689.04 - 72.6 x 9.8 = 7.41 a

a = - 3.03 m/s2

using the equation

h3 = Vo t + (0.5) at2

h3 = (29.6) (10) + (0.5) (- 3.03) (10)2

h3 = 144.5 m

Total height gained

H = h1 + h2 + h3 = 148 + 296 + 144.5 = 588.5 m

Change in gravitational PE = m g H = 72.6 x 9.8 x 588.5 = 4.2 x 105 J

2.

W = true weight = mg = 72.6 x 9.8 = 711.5 N

3.

Upward

4.

a = 2.96 m/s2

5.

148 m   upward

6.

29.6 m/s ,

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