elastic potential energy problem?
You are asked to design a spring that will give a 1160 kg satellite a speed of 2.85 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.
What must the force constant of the spring be?
What distance must the spring be compressed?
I know that F=ma.
PE= 1/2kx^2
but I don't understand how you can find the constant without knowing the compression.. or vise versa. HELP please?
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<< What must the force constant of the spring be? >>
Kinetic energy of satellite = Energy from the spring
(1/2)(m)(V^2) = (1/2)kx^2
where
m = mass of the satellite = 1160 kg (given)
V = velocity of satellite = 2.85 m/sec (given)
k = spring constant
x = length at which spring needs to be compressed
Substituting values,
(1/2)(1160)(2.85^2) =(1/2)(k)(x^2)
kx^2 = 9422.1 --- call this Equation 1
Using Newton's 2nd Law of Motion,
F = ma
kx = ma
where
a = acceleration of the satellite
and all the terms have been previously defined.
and substituting values,
kx = (1160)(5 * 9.8) = 56840
and solving for "x"
x = 56840/k ---call this Equation 2
Substituting Equation 2 in Equation 1, you will have
k(56840/k)^2 = 9422.1
Simplifying the above,
(56840)^2/k = 9422.1
k = (56840)^2/9422.1
k = 342,894 N/m
<< What distance must the spring be compressed? >>
You can use either Equation 1 or Equation 2 to solve for this. I trust that you can proceed from here on your own.