Newton’s second law of motion- The acceleration produced in the body by the action of a force acting on it is directly proportional to the force and inversely proportional to the mass of the body. It can also be started as: The rate of change of momentum is equal to the force applied to the body and the change in momentum always takes place in the direction of the force.
Verification: We take an inclined plank, which ends in a horizontal plank as shown in the figure. We place an iron ball at a height on the inclined plank and release it. It starts rolling down the inclined plank. After reaching the lower end of the inclined plank, it keeps on rolling on the horizontal plank and strikes the lead ball placed at some distance from the lower end of the inclined plank. Due to the collision, the lead ball moves some distance before coming to rest, we note down this distance.
Now, we take an aluminium ball in place of lead ball, whose diameter is equal to the diameter of the lead ball and place it at the point where the lead ball was earlier placed on the horizontal plank before being struck by the iron ball. It is also hit by the same iron ball, rolling down from the inclined plank from the same height as in the previous case. We note down the distance moved by the aluminium ball, after colliding with the iron ball. We find that distance moved by the aluminium ball is greater than the distance moved by the lead ball.
The iron ball on striking the lead and aluminium balls pushes them with the same force. Since the mass of aluminium ball is less than that of the lead ball, it means that when the same force acts on two bodies of different masses, lighter one will experience more acceleration than the heavier one. Hence, we conclude that in a body acceleration produced by a force is inversely proportional to the mass of the body, i.e.
a ∝ \(\frac{F}{m}\) ....(i)
Now we take two balls, one of iron I and other of aluminium of the same diameter and let them strike a glass marble placed at the same point on the horizontal plank separately. After rolling them from the same point of the inclined plank, we find that the iron ball imparts greater velocity to the marble then the aluminium ball, hence it means that iron ball applies greater force than aluminium ball. This leads us to the conclusion that acceleration is proportional to the force acting on it. Hence, a ∝ F … (ii)
Combining (i) and (ii), we get
or F ∝ ma or F = Kma .
We select the unit of force, in such a way that the value of K becomes one. Hence, F = ma.
This relation can also be obtained from Newton’s second law. Hence, Newton’s second law of motion is verified.
