Question

A rocket of mass 120 kg is fired in the gravity free space. It ejects gases with velocity 600 m/s at the rate of 1 kg/s, what is the initial thrust on the rocket ?

Answer 1

Here,

M = 120 kg

u = 600 m/s

dm/dt = -1 kg/s

negative because mass is decreasing with time

From Rocket propulsion analysis we have

mdv = -udm

=> dv/dm = -u/m  ---1.

We know from Momentum equation

Let m be the mass of the rocket at an instant and v its velocity at instant

F = d/dt(mv)

  = v(dm/dt) + m(dv/dt)

Using chain rule

dv/dt = (dv/dm)(dm/dt)

  F = v(dm/dt) + m(dv/dm)(dm/dt)

Using eqn. 1

  = v(dm/dt) + m(-u/m)(dm/dt) 

  = v(1) – u(-1)

  = v + u

At the beginning velocity of the rocket was 0,

v = 0

F =  u = 600

So initial thrust = 600 N

Initial acceleration = 600/120 = 5 ms-2

Answer 2

M=120kg, v=600m/s

A=5m/s^2