Question

You are asked to design a spring that will give a 1110 kg satellite a speed of 3.55 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00g. The spring's mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible.

(a) What must the force constant of the spring be?
(b) What distance must the spring be compressed?

Answer 1

Step-by-step explanation:

Kinetic energy of satellite = 1/2 m v²

= .5 x 1110 x 3.55²

= 6994.39 J

This energy comes from the elastic energy of compressed spring

elastic energy = 1/2 k d² where k is elastic constant and d is compression in spring .

1/2 k d² = 6994.39 J

kd² = 13988.77 --------------------------- (1)

force created by spring = k d

acceleration = force / mass

= k d / 1110

Given ,

k d / 1110 = 5 x g = 5 x 9.8 = 49

kd = 54390 ------------------------------------------------- ( 2 )

dividing ( 1 ) and ( 2 )

d = 13988.77 / 54390

= .25719 m

= 25.72 cm

kd = 54390

k x .25719 m = 54390

k = 211477.9 N /m