Question

How does a karate player break an ice slab in a single blow?

Answer 1

To understand this phenomenon, we have to understand the statement of the Second’s Law of Newton’s laws of motion, which says that –
The rate of change of momentum in a body is directly proportional to the force applied on the body.
$F = \dfrac{{dP}}{{dt}}$
where P = momentum.

Complete answer:
The momentum of a body defines the effect that a body possesses by the virtue of its mass and the velocity it is moving, and mathematically, it is the product of mass and velocity.
Momentum,
$P = mv$
where m = mass and v = velocity.
The force is defined as the rate of change of momentum per unit time.

Given that the momentum represents the effect or impact that the body possesses by the virtue of its velocity, the force can be defined as the realisation of the impact that the momentum of the body possesses.

This implies that for the karate player to break the slab of ice, he has to apply a huge amount of force, which is high enough to break the ice slab.

In order to do that, the karate player has to impart a huge momentum to the ice slab.

Since the karate player does not have a huge mass in his hands or strong enough to break it, the only way to impart a huge momentum change is to increase the velocity of his strike.

Therefore, the karate player has to impact the blow with a very fast pace in order to cause a huge change in the momentum, resulting in a higher amount of force, enough to break the ice slab.

It can be observed that the ice slab cannot be broken, even by the strongest man, if he strikes the slab with a low speed.

Hence, the karate player should strike the ice slab with a very high speed to break it.

Note: Another way to look at this problem is by the concept of impulse. The impulse is defined as the force multiplied by the time taken to apply by the force. If the force is applied in a shorter instance of time, the impulse is higher and hence, the impact of the force is greater than applying the same amount of force, in a longer instance of time. For example, if a player takes 1 seconds to strike a blow to break the ice slab, he will not be able to break the slab if he takes 3-4 seconds to strike the blow because the impulse is lesser.