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 × 104 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.

Part a)

Mass expelled by the rocket is given as

Part b)

Momentum that is carried away by the gases is given as

Part c)

Expression for the force is given as

Explanation:

As we know that the rate of mass expelled from the rocket is given as

speed of the rocket is constant and given as

Part a)

Since mass is expelled from the rocket at constant rate so total mass expelled in the time interval is

Part b)

As we know that momentum is the product of mass and velocity

So we have

Part c)

As we know that rate of change in momentum is known as force

So we will have

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