Question 1.
A rocket burns 0.01 kg of fuel each
second and ejects it as a gas with a velocity of 5, 000 m/s. What force does the
gas exert on the rocket?
Solution:
The momentum of the burning fuel
provides the force that moves the rocket forward.
Momentum of the burning fuel
= mv
= 0.01 x 5, 000
= 50 kgm/s
Therefore, the force the gas exerts on
the rocket each second is 50 Newtons.
Question 2.
A jet engine develops a thrust of 270 Ns
when the velocity of the exhaust gases relative to the engine is 300 ms^{1}.
What is the mass of the material ejected per second?
Solution:
The thrust on the jet engine is equal to
the momentum of the burnt gases.
Therefore,
Thrust = mv
270 = m x 300
m = 270/300
m = 0.9 kg
The mass of the material ejected per
second is 0.9 kg
Question 3.
A rocket
burns fuel at the rate of 10 kgs^{1} and ejects it with a velocity of 5
x 10^{3} ms^{1}. The Thrust exerted by the gas on the rocket
is?
Solution:
The momentum
of the burning gas equals the thrust exerted on the rocket.
Momentum = mv
Momentum of
burning fuel = 10 x 5 x 10^{3}
= 5 x 10^{4 }Ns
Therefore, Thrust exerted by the gas on
the rocket is
5.0 x 10^{4} Ns
Question 4.
A machine gun with a mass of 5 kg fires
a 50 g bullet at a speed of 100 ms^{1}, the recoil speed of the machine
gun is?
Solution:
The momentum of the bullet is equal to
the momentum of the gun.
MV = mv
Where M = mass of the gun, V = recoil
velocity (or speed) of the gun, m= mass of the bullet, v = velocity (or speed)
of the bullet.
Therefore,
5 x V = 0.05 x 100
V = 0.05 x 100/5 = 1
The recoil speed of the machine gun is 1
ms^{1}.
Note: the mass of the bullet has to be
converted from grams to kilograms. i.e., from 50 g to 0.05 kg.
Question 5.
If fuel was consumed at a steady rate of
5.0 x 10^{2} kg per second in a rocket engine and ejected as a gas with
a speed of 4 x 10^{3} ms^{1}, what is the thrust on the rocket?
Solution:
The thrust on the rocket is equal to the
momentum of ejected gas.
Momentum of ejected gas
= mv
= 5.0 x 10^{2} x 4 x 10^{3}
= 2.0 x 10^{2}
= 200 Ns
