Question

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.

Answer 1

Answer:

Part a)

Mass expelled by the rocket is given as

$\Delta m = R\Delta t$

Part b)

Momentum that is carried away by the gases is given as

$\Delta P = R\Delta t v$

Part c)

Expression for the force is given as

$F = R v$

$F = 5.85 \times 10^7 N$

Explanation:

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

$R = 1300 kg/s$

speed of the rocket is constant and given as

$v = 4.5 \times 10^4 m/s$

Part a)

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

$\Delta m = R\Delta t$

Part b)

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

So we have

$\Delta P = \Delta m v$

$\Delta P = R\Delta t v$

Part c)

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

So we will have

$F = \frac{\Delta P}{\Delta t}$

$F = R v$

$F = 1300 (4.5 \times 10^4)$

$F = 5.85 \times 10^7 N$