Question

A 30.0 kg mass is traveling to the right with a speed of 2.40 m/s on a smooth horizontal surface when it collides with and sticks to a second 30.0 kg mass that is initially at rest but is attached to one end of a light, horizontal spring with force constant 170.0 N/m. The other end of the spring is fixed to a wall to the right of the second mass.

a)Find the frequency of the subsequent oscillations.

b)Find the amplitude of the subsequent oscillations.

c)Find the period of the subsequent oscillations.

d)How long does it take the system to return the first time to the position it had immediately after the collision?

Answer 1

here,

the mass of first block , m1 = 30 kg

the mass of second block , m2 = 30 kg

initial velocity of first , u = 2.4 m/s

let the final velocity after the collison be v

using conservation of momentum

m1 * u = (m1 + m2 ) * v

30 * 2.4 = (30 + 30) * v

v = 1.2 m/s

spring constant , K = 170 N/m

A)

the frequency of the subsequent oscillations , f = 1/2pi sqrt(K/m)

f = 1/2pi * sqrt(170/(30+30)) Hz

f = 0.27 Hz

B)

let the amplitude of motion be A

v = A * (2*pi*f)

1.2 = A * ( 2*pi*0.27)

A = 0.71 m

the amplitude of motion is 0.71 m

C)

the period of subsequent oscillations , T = 1/f

T = 1/0.27 s = 3.7 s

D)

the time taken to return the first time to the position it had immediately after the collision , t = T = 3.7 s