a body hangs from a spring balance supported from the roof of an elevator .(a)

if the elevator has an upward accelaration of 2 m/s2 balance reads240 N. what is the true weight of the body?

under what circumstances will the balance read 160 N?

what will be the balance reading if the elevator cable breaks?

(a)

Suppose the mass of the body is m.

The actual weight of the body is W = mg = 9.8m

When the elevator accelerates upward, the pseudo force downward will be F ^{ / } = ma = m x2=2m

The net weight read by the spring balance is = 240 N

So,

240 = 9.8m + 2m

=> m = 20.34 kg

So, the true weight is, W = mg = 199.3 N

(b)

Let the acceleration be ‘a’ for the apparent weight be 160 N.

Now,

Apparent weight = Actual weight + pseudo force =mg +ma

=> 160 = 199.3 + (20.34)a

=> a = -1.93 m/s ^{ 2 }

The negative sign implies the elevator is now moving downward.

(c) The spring balance would read zero if the cable breaks, as the elevator, the spring balance and the body would remain in free fall and be weightless.

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