Q8 of 31 Page 358

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?

Given


Mass of the spring balance,M = 50 kg,


Length of the scale,Y = 20 cm = 0.2 m,


Period of oscillation,T = 0.60 seconds.


We know,


F = ky or M = ky i.e


Mass ×acceleration due to gravity = Spring constant × Length of scale.


Hence, k = Mg/0.2


= 50×9.8/0.2 N/m


= 2450 N/m


Now, T = 2π√m/k


T2 = 4π2m/k


Hence, m = T2k/4π2


Substituting the values we get,


m = kg = 22.3 kg


Hence, mg = 218.5 N = 22.3 kgf.


More from this chapter

All 31 →
6

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a = 0.7x


(b) a = –200x2


(c) a = –10x


(d) a = 100x3

7

The motion of a particle executing simple harmonic motion is described by the displacement function,

x(t) = A cos (ωt + φ).


If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle? The angular frequency of the particle is π s–1. If instead of the cosine function, we choose the sine function to describe the SHM x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

9

A spring having with a spring constant 1200 N m–1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.


Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.

 10

In Exercise 14.9, let us take the position of mass when the spring is unstreched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is

(a) at the mean position,


(b) at the maximum stretched position, and


(c) at the maximum compressed position.


In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?