Newton’s Laws of Motion - Newton's Second Law of Motion

When one object strikes another, the impact depends on the mass and velocity of the striking object. This combination of mass and velocity is called momentum.

Momentum is represented by the formula:

P = m × v

where $P$ is momentum, $m$ is mass, and $v$ is velocity.

Momentum is a vector quantity, meaning it has both magnitude and direction. Its direction is the same as the velocity of the object.

Units of Momentum:

• SI system: kg⋅m/s
• CGS system: g⋅cm/s

Newton's second law states that the rate of change of momentum is proportional to the applied force, and the change occurs in the direction of the force.

Suppose an object of mass m has an initial velocity u. When a force F is applied in the direction of its velocity for time t, its velocity becomes v.
The initial momentum of the object = mu,
 Its final momentum after time t = mv

Rate of change of momentum =`"Change in momentum"/"Time"` 

Rate of change of momentum =`"mv- mu"/"t"`=`"m (v- u) "/"t"`=ma

According to Newton’s second law of motion, the rate of change of momentum is proportional to the applied force.

ma ∝ F

F = k ma (k = constant of proportionality and its value is 1).
F = m × a

Consider two objects having different masses that are initially at rest. The initial momentum for both is zero. Suppose a force ‘F’ acts for time ‘t’ on both objects. The lighter object starts moving faster than the heavier object.

However, from the above formula, we know that the rate of change of momentum, i.e., ‘F’ in both objects, is the same and the total change in their momentum will also be the same, i.e., ‘Ft’. Thus, if the same force is applied to different objects, the change in momentum is the same.

In the SI system, the unit of force is Newton.

• Newton (N) : The force necessary to cause an acceleration of 1 m/s² in an object of mass 1 kg is called 1 Newton. 1 N = 1 kg × 1 m/s²

In the CGS system, the unit of force is a dyne.

• Dyne: The force necessary to cause an acceleration of 1 cm/s² in an object of mass 1 gm is called 1 dyne.
  1 dyne = 1 g × 1 cm/s²

1. Activity A:

• Drop a plastic ball and a rubber ball from the same height.
• Catch both balls.

Observation: The plastic ball is easier to catch because it has less mass and thus less momentum compared to the rubber ball.

2. Activity B:

• Catch a ball thrown at slow speed.
• Catch the same ball thrown at high speed.

Observation: The ball thrown at slow speed is easier to catch because it has less momentum (P=m×v), reducing the impact force on your hands.

3. Conclusion:

A ball with less momentum (due to lower mass or speed) is easier to catch. Momentum determines the difficulty of handling an object in motion.