A karate player breaks a slab of ice with a single blow. This is possible because:

The correct option is

The large momentum of the hand is reduced to zero in a very short time.

Explanation

The phenomenon is governed by Newton’s Second Law of Motion and the concept of Impulse. According to Newton’s Second Law, the force applied is directly proportional to the rate of change of momentum ($F = \frac{\Delta p}{\Delta t}$). Impulse is defined as the product of force and the time duration over which it acts ($J = F \times \Delta t = \Delta p$).

Detailed Analysis:

• The force is applied over a long duration to maximize impact. is Incorrect: If the force were applied over a long duration, the rate of change of momentum would be low, resulting in a smaller impact force. This is the principle used in shock absorbers or catching a cricket ball, where time is increased to reduce force.
• The large momentum of the hand is reduced to zero in a very short time. is Correct: A karate player strikes the ice slab with a hand moving at high velocity, possessing large momentum. Upon contact, the hand is brought to a halt almost instantly. This means the large change in momentum ($\Delta p$) occurs in an extremely short time interval ($\Delta t$). Since Force is inversely proportional to time for a constant change in momentum ($F \propto \frac{1}{\Delta t}$), the resulting force exerted on the ice is extremely large, sufficient to break the slab.
• The ice slab possesses negligible inertia. is Incorrect: The ice slab has mass and therefore possesses inertia. The breaking is due to the magnitude of the external force, not a lack of inertia.
• The player utilizes the gravitational force of the earth. is Incorrect: While gravitational force acts on the player, the breaking of the ice is primarily due to the muscular force converted into kinetic energy and subsequently into an impulsive force, not the gravitational pull of the earth.

Key Takeaway:

To generate a large impact force from a fixed change in momentum, the time of contact must be minimized. This application of Impulse allows a karate player to exert a force far exceeding their static strength.