QS Study

Application of Newton’s Laws of Motion

When a body applies force on another body then the second body also applies equal and opposite force on the first body. We have learnt about this action and reaction forces from Newton’s third law of motion. In nature forces act in couples. In nature there is not individual separate force. Two forces are complementary to each other. One of these forces is called action force and the other one is reaction force. As long as action force is there, there exists reaction force also. Practical application of Newton’s laws of motion is described below with example.

Firing of a bullet from a gun: When a bullet is fired from a gun, the bullet moves ahead with tremendous speed. If the gun applies force F on the bullet, the bullet also applies equal and opposite force on the gun. Due to this reaction force the gun also recoils backward [Figure].

Fig: Backward Velocity of gun and Forward Velocity of gun

This can be explained by momentum as well. Before firing both the gun and the bullet remain at rest. So momentum of both the gun and bullet is zero. Hence their total initial momentum is zero. After firing, due to explosion, the bullet moves ahead with a velocity. So it gets a forward momentum. Now, according to conservation principle of momentum total momentum after firing will be zero. So, the gun will also acquire an equal and opposite momentum. Then the gun, of course, will get a backward motion [Figure].

Let the bullet of mass m is released with velocity v from a gun of mass M. Again, suppose the velocity of the gun after firing = V.

Before firing their total momentum = 0

After firing their total momentum = momentum of the gun + momentum of the bullet

= MV + mv

But according to the conservation principle momentum before and after must be equal.

so, MV + mv = 0

then, mv = – MV = M(-V)

That means, (mass of the bullet x velocity of the bullet)

= (mass of the gun x recoil velocity of the gun)

From this equation it can be said that velocity of the bullet > recoil velocity of the gun.