Rocket attatched to a spring problem

[mjolnir80]

Homework Statement

a 10.2 kg weather rocket generates a thrust of 200N. the rocket ,pointing upwards, is clamped to the top of a vertical spring, whose spring constant is 500N/m and is anchored to the ground
a)initially before the engine is ignited the sits at rest on top of the srping. how much is the spring compressed?
b)after the rocket has ignited what is the speed when the spring has stretched 40 cm?

Homework Equations

The Attempt at a Solution

for part a i calculated 20cm compression for the spring
for part b do we have to consider the pushing force from the 20 cm compression as the rocket is being launched?
and also is the elastic energy of the spring acting against the kinetic energy of the rocket (in other words do we have to subtract them at the 40 cm mark?)

 

[Doc Al]

for part a i calculated 20cm compression for the spring

Good.

for part b do we have to consider the pushing force from the 20 cm compression as the rocket is being launched?
and also is the elastic energy of the spring acting against the kinetic energy of the rocket (in other words do we have to subtract them at the 40 cm mark?)

Since the rocket is attached to the spring, you definitely must consider the force it exerts on the rocket.

I recommend that you set up an energy equation to solve for the rocket's kinetic energy at the point in question.

 

[wimma]

I recommend that you set up an energy equation to solve for the rocket's kinetic energy at the point in question.

Hmm. Way easier just to use calculus and the fact that a = (vdv)/dx
Then you just set up a simple problem with uniform resisted motion where the force (taking up as positive) is given by F = T - mg - kx
Where T is the thrust of the rocket, mg is its weight (assuming that it doesn't lose mass in the expulsion of fuel, otherwise the weight is g(dm/dt)), k is the spring constant.

Then u just apply Newton's 2nd so that F=ma and proceed... seems easier than worrying about energy IMHO.

 

[Doc Al]

Hmm. Way easier just to use calculus...

Calculus!

seems easier than worrying about energy IMHO.

There's certainly nothing wrong with integrating the net force on the rocket, but I don't see how that's easier. If you're familiar with the expression for energy stored in a spring, you can dispense with any integration and write down the final energy expression in one step. No calculus needed. (Of course, you'd need calculus to derive the expression for spring potential energy.)

 

[3ephemeralwnd]

how did you do part a?

 

[Doc Al]

how did you do part a?

Use Hooke's law.

 

[3ephemeralwnd]

i tried using energy .. Eg lost by rocket = Ee gained by spring
but i got 40 cm instead of 20 (why is this wrong?)

and how would you solve the problem using hooke's law?

 

[Doc Al]

i tried using energy .. Eg lost by rocket = Ee gained by spring
but i got 40 cm instead of 20 (why is this wrong?)

This is a force problem, not an energy problem. The rocket is just resting on the spring.

and how would you solve the problem using hooke's law?

What force is compressing the spring?

 

[3ephemeralwnd]

oh, the force of gravity..

so Fg = Fs? but doesn't that mean Fnet is 0

 

[Doc Al]

so Fg = Fs? but doesn't that mean Fnet is 0

Sure. The net force on the rocket is zero while it's resting on the spring.