A 92 kg astronaut and a 1200 kg Satellite are at rest relative to the space shut

Question

A 92 kg astronaut and a 1200 kg Satellite are at rest relative to the space shuttle. The astronaut pushes the satellite, giving it a speed of 0.14 m/s directly away from the shuttle. After 7.5 s, the astronaut comes into contact with the shuttle. What was the initial distance between the shuttle and the astronaut? A 0.430 kg block is attached to a horizontal, unstretched spring, whose force constant is 20.0 N/m. The block rests on a frictionless surface. A 0.050 kg wad of putty is thrown horizontally at the block, hitting it with a speed of 2.3 m/s and sticking to it. How much does the putty-block system then compress the spring?

Explanation / Answer

From the given question,

mass of astrounaut (m1)=92kg

mass of satellite(m2)=1200kg

velocity of satellite(v2)=0.14m/s

by conservation of momentum,

m1v1=m2v2

92 * v1= 1200 * 0.14

v1=1.826 m/s

time taken to reach space shuttle(t)=7.5s

distance= speed x time

=1.826 x 7.5

=13.69m

Initial distance between shuttle and astronaut is 13.69m.

b) mass of block(m1)=0.430kg

Force constant of spring(k)=20N/m

mass of putty(m2)=0.05kg

velocity of putty at the time of hitting(v2)=2.3m/s

by conservation of momentum,

m2v2=(m1+m2)v

0.05 x 2.3= (0.43+0.05)v

v=0.24 m/s

using conservation of energy

1/2 (m1+m2) v2 = 1/2 k x2

(0.43 + 0.05) (0.24)2 = (20) (x2)

x=0.037m

or x=3.7cm

The putty block system compress the spring by 3.7cm.

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