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wulfsdad
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Homework Statement
This is generalized from problem # 11.52 from "Physics: For Scientists and Engineers: A Strategic Approach" By Randall D. Knight 2nd Ed.
An (M) kg weather rocket generates a thrust of (F) N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is (K) N/m, is anchored to the ground.
There are 3 parts:
A) finding the spring's initial compression (y) with the rocket resting on it,
B) find rocket's speed (V) when spring is stretched (d) m, and
C) "For comparison, what would be the rocket's speed after traveling this distance if it weren't attached to the spring? "
Homework Equations
K_{f} + U_{f} + \DeltaE_{th} = K_{i} + U_{i} + W_{ext}
\DeltaK = W_{net}
W = \vec{F} \bullet \Delta\vec{s}
The Attempt at a Solution
I got part A: finding the spring's initial compression (y).
Mgy = Ky^{2} \rightarrow Mg = Ky \rightarrow y = \frac{Mg}{K}
Then part B: finding rockets speed (V) when the spring is stretched (d) m.
\frac{1}{2}MV^{2} + Mg( y + d ) + \frac{1}{2}Kd^{2} = \frac{1}{2}Ky^{2} + F( y + d )
So for part C: find the rocket's speed (v) after traveling this distance if it weren't attached to the spring?
I used the same equation as B but with the spring removed:
\frac{1}{2}MV^{2} + Mg( y + d ) = F( y + d )
This was incorrect. I also tried it with just ( d ), instead of ( y + d ).
Then I tried reasoning that:
F = MA --> A = F/M
Then using kinematics:
2\frac{F}{M}( y + d ) = v^{2}
This was also incorrect.