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Calculating Force Based On Newton's Third Law Of Motion (1)

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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 103 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 103

= 5 x 104 Ns

Therefore, Thrust exerted by the gas on the rocket is        5.0 x 104 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 103 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 103

= 2.0 x 102

= 200 Ns