uestion 3 c) 3of6 Part A You are asked to design a spring that will give a 1290

Question

uestion 3 c) 3of6 Part A You are asked to design a spring that will give a 1290 kg satellite a speed of 3.45 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum spring's mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible. What must the force constant of the spring Take the free fall acceleration to be g 9.80 m/s be? of 5.00g. The 0? /m PartB What distance must the spring be compressed? Next >

Explanation / Answer

Here, the maximum force on the satellite, F = ma = 1290 x 5.00 x 9.80 = 63210 N
This is equal to the maximum spring force (kx)

which means -

kx = 63210 -----------------------------------------------(i)

again -
The kinetic energy the satellite gains can be found using Ek=1/2mv^2=1/2 x 1290 x 3.45^2 = 7677 J

This kinetic energy must come from the elastic potential energy 1/2kx^2, so by conservation of energy
1/2kx^2 = 7677

=> kx^2 = 15354 ---------------------------------------(ii)

Now, do (ii) / (i) -

x = 15354 / 63210 = 0.243 m

This is the answer of Part B.

Now for Part A -

k = 63210 / 0.243 = 260123 N/m

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