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Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 N for the first 3.0 s after the elevator starts moving, then 930 N for the next 3.0 s. What is the elevator鈥檚 velocity 6.0 s after starting?

Short Answer

Expert verified

The velocity of the elevator after 6sis 3.3m/sdownward.

Step by step solution

01

Given information

Henry's mass-m=95kg

The scales reads 830Nfor the first 3.0safter the elevator starts moving, then 930Nfor the next 3.0s.

02

Calculation of elevator velocity

We know that, According to Newton's second law,

F=ma

From this; a=Fmeq.1

Writing equation of motion,

localid="1649614779244" Vf=vo+ateq.2

substituting eq.1in eq.2

localid="1649614793717" Vf=vo+Fmteq.3

Now, Before starting 3sec.assuming v0=0

After starting 3sec.The net forcelocalid="1649615010224" role="math" F=830-959.81=-101.95N

Therefore, substituting the values of initial velocity and net force on eq.3we get

localid="1649615237271" Vf,t=3=-101.95953=-3.22eq.4

Now after 3sec.interval the net force localid="1649615359767" F=930-959.81=-1.95N.

For final velocity after role="math" localid="1649615528476" 6sec.substitute in eq. 3.

localid="1649615570159" role="math" Vf,t=6=-1.95953=-0.06eq.5

Summing eq.4and eq.5

localid="1649615654824" Vf=-3.22-0.06Vf=-3.28Vf=-3.3m/s

Velocity containing negative value is downward which means, the elevator is moving down or descending.

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