2. Consider a situation where change in momentum come from a change in mass rather than that
coming from a change in velocity of an object: rocket propulsion. The propelling gases exert force
on the rocket. The gases are expelled at a rate of R = 1300 kg/s with a speed of v = 4.5 × 10^4
m/s.
a) What is the mass expelled in time ∆t. Label this mass ∆m.
b) How much momentum does the mass carry, in terms of ∆t, R, and v.
c) Use the relationship between the average force and change in momentum to obtain the
expression for the average force in terms of R and v and calculate its value

a) [kg]

b)

c) F = vR,

Explanation:

a)

In this problem, we are given the rate at which the mass is expelled by the rocket:

Therefore, the total mass expelled by the rocket in a time is the given by the equation

where

is the mass expelled

R is the rate at which it is expelled

is the time interval

Here we have

R = 1300 kg/s

Therefore, substituting into the equation,

[kg]

b)

The momentum of an object is given by

where

p is the momentum

m is the mass of the object

v is the velocity of the object

In this problem, we want to find the momentum carried by the mass of the gas, , that is expelled by the rocket.  This will be given by

where

is the mass of gas expelled in a time of

is the velocity of the gas

Substituting,

c)

According to Newton's second law of motion, the average  force exerted on an object is equal to its rate of change of momentum:

where

F is the average force

is the change in momentum

is the time interval

In this problem, the change in momentum of the rocket is equal to the momentum of the gas expelled, so:

Substituting into the equation, we can therefore find the average force on the rocket:

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