Question

Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 N for the first 3.6 s after the elevator starts moving, then 930 N for the next 3.6 s.

What is the elevator's velocity 4.0 s after starting?

Answer 1

Answer:
`3.816\ m/s`

Step-by-step explanation:

Given

Mass of Henry is 95 kg

Normal weight of Henry is
`mg=95* 9.8=931\ N`

The scale reads the weight as 830 N for first 3.6 s i.e. less than the normal weight i.e. Elevator is moving downwards

Apparent weight is given by

`\Rightarrow 830=m(g-a)\quad [a=\text{acceleration of elevator}]\\\Rightarrow 830=95(9.8-a)\\\Rightarrow 8.736=9.8-a\\\Rightarrow a=1.06\ m/s^2`

After 3.6 s weight becomes 930 N which is approximately equal to normal weight. It implies elevator starts moving with constant velocity i.e. no acceleration.

If elevator starts from rest, it velocity after 3.6 s is

`v=u+at\\\Rightarrow v=0+1.06(3.6)\\\Rightarrow v=3.816\ m/s`

This velocity will remain continues as after 3.6 s, elevator starts moving with constant velocity.