Question

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?

Answer 1

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 × 9.8 = 490

∴Spring constant, `k = F/l = 490/0.2 = 2450 Nm^(-1)`

Mass m, is suspended from the balance.

Time Period, `T = 2pi sqrt(m/k)`

`:. m = (T/(2pi))^2 xx k = (0.6/(2xx3.14))^2 xx 2450 = 22.36 kg`

∴Weight of the body = mg = 22.36 × 9.8 = 219.167 N

Hence, the weight of the body is about 219 N.

Answer 2

M = 50 kg, y = 20 cm = 0.2 cm, T = 0.60 s

F = ky or Mg =  ky or `k = (Mg)/0.2 = (50xx 9.8)/0.2 Nm^(-1)`

or `K  = 2450 Nm^(-1)`

Now `T = 2pi sqrt(m/k)`

or `T^2 = 4pi^2 m/k ` or `m = (T^2k)/(4pi^2)`

or  `m = (0.6 xx 0.6 xx 2460 xx 49 )/(4xx484) kg = 22.3 kg`

`=> mg = 22.3 xx 9.8 N = 218.5 N = 22.3 kgf`