A 10.4kg weather rocket generates a thrust of 240N . The rocket, pointing upward

Question

A 10.4kg 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 600N/m , is anchored to the ground.

Part A

Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?

I got 0.17m, which I know is correct.

Part B

After the engine is ignited, what is the rocket's speed when the spring has stretched 34.0cm ?

Part C

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

Explanation / Answer

A) here the rocket is in equilibrium

Fnet = 0

F_spring - F_gravity = 0

k*x - m*g = 0

x = m*g/k

= 10.4*9.8/600

= 0.17 m

B)
According to work-enrgy theroem
Wnet = K2 - K1

W_thrust - W_gravity - W_spring = K2- K1

240*(0.34+0.17) - 10.4*9.8*(0.34+0.17) - 0.5*600*(0.34^2-0.17^2) = 0.5*m*(v2^2-v1^2)

44.41 = 0.5*m*v2^2 (here v1 = 0)

v2 = sqrt(2*44.41/10.4)

= 2.92 m/s

C)
According to work-enrgy theroem
Wnet = K2 - K1

W_thrust - W_gravity + W_spring = K2- K1

240*(0.34+0.17) - 10.4*9.8*(0.34+0.17)+0.5*600*0.17^2 = 0.5*m*(v2^2-v1^2)

79.09 = 0.5*m*v2^2 (here v1 = 0)

v2 = sqrt(2*79.09/10.4)

= 3.9 m/s <<<<<<<<<<<----------------------Answer

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