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?

Asked by Pragya Singh | 1 year ago |  78

##### 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 =$$\dfrac{F}{I}$$

$$\dfrac{490}{0.2}$$

We get,

= 2450 N m-1

Mass m is suspended from the balance.

Time period, t = $$\dfrac{2π\sqrt{m}}{k}$$

Therefore,

m =  $$( \dfrac{T}{2π})^2$$x k

= $$( \dfrac{0.6}{(2 \times 3.14)})^2$$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

Answered by Abhisek | 1 year ago

### Related Questions

#### A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction

A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x0 and v0. [Hint: Start with the equation x = a cos (ωt+θ) and note that the initial velocity is negative.]

#### A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is

(a) 5 cm

(b) 3 cm

(c) 0 cm.

#### A circular disc of mass 10 kg is suspended by a wire attached to its centre.

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant α is defined by the relation J = –α θ, where J is the restoring couple and θ the angle of twist).

#### Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals.

Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

#### You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation

You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of

(a) the spring constant k and

(b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.