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turtledove
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Homework Statement
A 10.2 kg weather rocket generates a thrust of 177.0 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 385.0 N/m, is anchored to the ground. Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed? (ANS: 0.26 m)
a) After the engine is ignited, what is the rocket's speed when the spring has stretched 12.0 cm past its natural length? (ANS: 2.78 m/s)
b) What would be the rockets speed after traveling the distance if it weren't tied down to the spring? (ANS: ?)
Homework Equations
W = Ef - Ei
Ee = 0.5 kx^2
Ek = 0.5 mv^2
Ep = mgh
The Attempt at a Solution
PART B ONLY:
[Fthrust x d] = [mgh + 0.5mv^2]f - [0]i
[(177)(0.26 + 0.12)] = [(10.2)(9.8)(0.26 + 0.12)] + [0.5(10.2)v^2]
v = 2.40 m/s <-- this is WRONG
I was able to solve PART A, but I don't know what to do when the rocket is not attached to the spring. I suppose it might be Vf^2 = Vi^2 + 2ad, but I don't know what distance to use. In my attempt, I just used the formula I used for PART A, WITHOUT the elastic energy added. Somebody pleaseee help me!