Please answer the following question. Item 5 You are asked to design a spring th

Question

Please answer the following question.
Item 5 You are asked to design a spring that will give a 1300 kg satellite a speed of 1.80 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. Part A What must the force constant of the spring be? Take the free fall acceleration to be g guso m/s2 Submit My Answers Give Up Part B What distance must the spring be compressed? Submit My Answers Give Up N/m back Continue

Explanation / Answer

here,

let the spring constant be k and distance be A

maximum accelration , a = 5 g = 49 m/s^2

A * w^2 = a

A * (sqrt(k/m))^2 = 49

A * k/1300 = 49 ....(1)

mass , m = 1300 kg

using conservation of energy

potential energy stored in the spring = kinetic energy gained by satellite

0.5 * k * A^2 = 0.5 * m * v^2

K * A^2 = 1300 * 1.8^2 ....(2)

from (1) and (2)

K = 9.6 * 10^5 N/m, A = 0.066 m

a)

the spring constant is 9.6 * 10^5 N/m

b)

the amplitude of oscillation is 0.066 m

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