A75.0kg person stands on a scale in an elevator. what does the scale read (in kg) when the elevator is (a) at rest, (b) ascending at a constant speed of 3.0m/s, (c) falling at 3.0m/s, (d) accelerating upward at 3.0m/s2 , (d) accelerating downward at 3.0m/s2 .

Explanation: Scale only reads reaction force so we will find out reaction force  of ground in different cases.

a ) Let R be the reaction force of floor  in the first case.

Net force = R - mg

= mass x acceleration = 0 ( body is at rest ).

R = mg , scale will read his actual weight.

In the  case of b) and c) also acceleration is zero hence

R - mg =0

R =mg ,scale will read his actual weight.

d) In this case there is acceleration of 3 m s⁻² in upward direction so

R - mg = ma

R = m( g+a) = 75 x ( 9.8 + 3 ) = 960 N

The reading of scale will be more than his actual weight .

It will read weight as 960/9.8 = 97.96 kg.

e) In this case body is going downwards

mg -R = ma

R = m ( g - a )

= 75 ( 9.8 - 3 )

= 435 N

= 435 / 9.8 kg

= 44.38 kg

So scale will read less than his actual weight.

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c. magnitude and direction