What is the thrust of the engine?

[NanoTech]

A rocket is moving away from the solar system at a speed of 6.0 x 10^3 m/s. It fires its engine, which ejects exhaust with a speed of 3.0 x 10^3 m/s relative to the rocket. The mass of the rocket at this time is 4.0 x 10^4 kg, and its acceleration is 2.0 m/s/s.

A) What is the thrust of the engine?

I thought to use the equation T = ma ? T = (4.0 x 10^4 kg)(2.0m/s/s) = 8.0 x 10^4 N.

B) At what rate, in kilograms per second, is exhaust ejected?

I'm stumped on this one, I thought that's what Thrust was?

I thought to maybe use the equation: Vf-Vi = Vrel ln(Mi/Mf) but i don't even know how to use it in this situation... Any help would be great, thanks! ~Dave

 

[Moose352]

I think you need to use momentum.

 

[Doc Al]

Originally posted by NanoTech
A) What is the thrust of the engine?

I thought to use the equation T = ma ? T = (4.0 x 10^4 kg)(2.0m/s/s) = 8.0 x 10^4 N.

Right. (Assuming that the gravitational force is negligible and that the thrust is the only force on the rocket.)

B) At what rate, in kilograms per second, is exhaust ejected?

I'm stumped on this one, I thought that's what Thrust was?

How could an exhaust rate be equal to a force? The units don't match.

Anyhow, thrust is given by V_rel*dM/dt.

 

[NanoTech]

ok, so for part B. i take the derivative of the mass, then multiply it by the Vrel. thanks. ~Dave

 

[Doc Al]

Originally posted by NanoTech
ok, so for part B. i take the derivative of the mass, then multiply it by the Vrel.

For part B you are to find the exhaust rate, which is dM/dt. Set the thrust equal to what you found in part A, then solve for dM/dt.