A 12.0kg weather rocket generates a thrust of 240N . The rocket, pointing upward

Question

A 12.0kg weather rocket generates a thrust of 240N . The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 490N/m , is anchored to the ground.

Part B: After the engine is ignited, what is the rocket's speed when the spring has stretched 40.0cm ?

Part C: For comparison, what would be the rocket's speed after traveling this distance if it weren't attached to the spring?

A 12.0kg weather rocket generates a thrust of 240N . The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 490N/m , is anchored to the ground. Part B: After the engine is ignited, what is the rocket's speed when the spring has stretched 40.0cm ? Part C: For comparison, what would be the rocket's speed after traveling this distance if it weren't attached to the spring? Help me with Part B and C please!

Explanation / Answer

initial compression y1 = Fg/k = (12*9.8)/490 = 0.24 m

Ue1 = 0.5*k*y1^2 = 0.5*490*0.24*0.24 = 14.112 J

Ug1 = 0

K1 = 0

at y2 = 40 cm = 0.4 m

Ue2 = 0.5*y2^2 = 0.5*490*0.4*0.4 = 39.2 J

Ug2 = m*g*(y1+y2) = 12*9.8*(0.24+0.4) = 75.264

KE2 =0.5*m*v^2 = 0.5*12*v^2 = 6*v^2

Wother = F*(y1+y2) = 240*(0.24+0.4) = 153.6 J

from energy conservation

dUe + dUg + dUk = Wother

(39.2-14.112)+(75.264-0)+(6v^2-0) = 153.6

v = 2.97 m/s

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part C

Ue2 = 0

dUe + dUg + dUk = Wother

(0-14.112)+(75.264-0)+(6v^2-0) = 153.6

v = 3.92 m/s

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