Question

A model rocket engine has an average thrust of 5.1 N. It has an initial mass of 38 g, which includes fuel mass of 10.5 g. The duration of the burn is 2.18 s. (a)What is the average exhaust speed of the engine?

(b) The engine is placed in a rocket body of mass 67.8 g and fired from rest in zero gravity by an astronaut in space. What is the rocket's final speed if fuel burns at a constant rate?

Answer 1

(a) Mass flow rate of the rocket `dotm=10.5/2.18\ gs^-1`
From Newton Third law of motion

Reaction force generated from exhaust of gases creates Thrust `T`

From Newton Second law of motion

`T= "Rate of change of momentum of exhaust gases"`
`=>T= (∆(mv)) / t` .....(1)

Let `V` be average exhaust speed of gases from the engine. (1) becomes

`T = ((∆m) V)/t`

Inserting given values we get

`5.1 = (10.5xx10^-3)/2.18xxV`
`=>V = 5.1xx2.18/(10.5xx10^-3)`
`=>V = 1058.9\ ms^-1`

(b) Total mass of engine and rocket `=38+67.8=105.8\ g`
Mass of engine and rocket `-` fuel`=105.8-10.5=95.3\ g`
Average mass which is accelerated `=100.55\ g`
Average acceleration produced `=5.1/(100.55xx10^-3)=50.72\ ms^-2`

Final speed is found with the help of kinematic expression

`v=u+at`

Inserting various values we get

`v=0+50.72xx2.18`
`=>v=110.6\ ms^-1`