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| Applications of Law of Conservation of Momentum, Newton's Third Law of Motion |
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| When a bullet is fired from a gun, the gases produced in the barrel exerts a tremendous force on the bullet (action force). As a result, the bullet moves forward with a great velocity called the muzzle velocity. The bullet at the same time exerts an equal force on the gun in the opposite direction (reaction force). Due to this the gun moves backwards. This backward motion of the gun is called the recoil of the gun. The velocity with which the gun moves backwards is called the recoil velocity. |
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| Recoil of Gun |
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| Let 'M' be the mass of the gun and m that of the bullet. Before firing both are at rest. After firing let 'V' be the velocity of the gun and 'v' that of the bullet. By law of conservation of linear momentum, |
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| initial momentum of gun and bullet = final momentum of gun and bullet. |
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| The initial momentum of the gun and the bullet is equal to zero since they are initially at rest. |
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| Final momentum after firing = MV + mv = 0 |
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| [The negative sign indicates that the gun is recoiling] |
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| The motion of a rocket is an application of Newton's third law of motion and law of conservation of linear momentum. |
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| A rocket is a projectile that carries the rocket fuel and the oxidiser, which supplies the oxygen needed for combustion. Liquid hydrogen, liquid paraffin etc., are used as rocket fuels and hydrogen peroxide, liquid oxygen etc., are used as oxidisers. The fuel-oxidiser combination in a rocket is called the propellant. |
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| The simplest form of a rocket consists of a combustion chamber in which a solid or liquid propellant is burnt. There is a nozzle at its tail through which the gaseous products of combustion can escape. The rocket forces a jet of hot gases downwards through the nozzle. This is the action. The jet of gases exerts an equal force on the rocket, pushing it forward. This is the reaction. This force gives the rocket a forward acceleration. |
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| Rocket Propulsion |
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| The operation of a rocket illustrates the conservation of momentum. Just before launching, the momentum of the rocket is zero. When the rocket is fired, it forces a jet of hot gases with a high velocity through the nozzle. The jet of gases acquires a momentum downwards. Hence, the rocket acquires a momentum of equal magnitude in opposite direction. Thus the rocket moves upwards. |
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| With a single stage rocket it is not possible to attain very high speed and hence multistage rockets are designed. In multistage rockets when the fuel of the first stage gets exhausted, the rocket casing is detached and dropped off and the second stage is ignited. |
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| 01. A force of 980 N acts on a body for 0.1 seconds. Calculate the change in momentum of the body. |
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| Solution: |
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| Force = 980 N |
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| Time for which the force acts = 0.1 s |
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| Change in momentum = impulse = Ft |
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| Therefore, change in momentum = Ft |
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| = 980 x 0.1 |
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| = 98 N S |
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| 02. A body of mass 10 kg moving with a velocity of 20 m/s along a straight line collides with another body of mass 8 kg moving in the same direction with a velocity of 5 m/s. After collision the velocity of the heavier body is 10 m/s. Calculate the final velocity of the other. |
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| Solution: |
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| By law of conservation of momentum, momentum before collision is equal to momentum after collision. |
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| m1 u1 + m2 u2 = m1 v1 + m2 v2 |
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| 10 x 20 + 8 x 5 = 10 x 10 + 8 x v2 |
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| 200 + 40 = 100 + 8v2 |
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| 240 = 100 + 8v2 |
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| 8v2 = 240 - 100 |
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| 8v2 = 140 |
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| i.e., velocity of the lighter body = 17.5 m/s |
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