Question
Asked Nov 28, 2019
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 A child of mass 43 kg stands on a scale inside an elevator.

Select one or more:

A. The scale would show his weight as 335.40 N when the elevator accelerates downward at 2 m/s2.
B. The scale would show his weight as 507.4 N when the elevator accelerates upward at 2 m/s2.
C. The scale would show his weight as 335.40 N when the elevator accelerates upward at 2 m/s2.
D. The scale would show his weight as 335.40 N when the elevator decelerates upward at 2 m/s2.
E. The scale would show his weight as 421.4 N when the elevator is stationary.
F. The scale would show his weight as 335.4 N when the elevator decelerates upward at 2 m/s2.
G. The scale would show his weight as 421.40 N when the elevator moves with a constant velocity of 2.5 m/s.
R
mg
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R mg

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Expert Answer

Step 1

Consider the acceleration of the elevator be a, and the speed of the elevator be v.

 

Apply Newton’s second law of the motion along the vertical direction, and solve for the normal reaction on the child, that is the weight shown by the scale, when the elevator accelerates downward at 2 m/s2.

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F=ma mg -R ma R =m(g-a) (43 kg) (9.8 m/s2-2 m/s2) 1N =335.4 kg.m/s2 1 kg m/s2 = 335.4 N

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Step 2

Apply Newton’s second law of the motion along the vertical direction, and solve for the normal reaction on the child, that is the weight shown by the scale, when the elevator accelerates upward at 2 m/s2.

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Image Transcriptionclose

F=ma R-mg m R m(g+a) (43 kg) (9.8 m/s2 +2 m/s2) 1N =507.4 kg m/s 1 kg m/s2 507.4 N =

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Step 3

Apply Newton’s second law of the motion along the vertical direction, and solve for the normal reaction on t...

help_outline

Image Transcriptionclose

F,ma R-mg a) R=m(g-a) =(43 kg) (9.8 m/s2-2 m/s2) 1N = 335.4 kg m/s 1 kg m/s2 =335.4 N

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