In: Physics

What is the weight of the body?

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

Solutions

Expert Solution

Given

Maximum mass that the scale can read, M = 50 kg

Maximum displacement of the spring = Length of the scale, l = 20 cm

= 0.2 m

Time period, T = 0.6 s

Maximum force exerted on the spring, F = mg

Where,

g = acceleration due to gravity = 9.8 m/s2

F = 50 x 9.8 = 490

Hence,

Spring constant, k = F / l

= 490 / 0.2

We get,

= 2450 N m-1

Mass m is suspended from the balance.

Time period, t = 2π√m / k

Therefore,

m = (T / 2π)2 x k

= {0.6 / (2 x 3.14)}2 x 2450

We get,

= 22.36 kg

Hence, weight of the body = mg = 22.36 x 9.8

On calculation, we get,

= 219.13 N

Therefore, the weight of the body is about 219 N

The weight of the body is about 219 N.

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