(a) Estimate the force with which a karate master strikes a...

(a) Estimate the force with which a karate master strikes a board, assuming the hand's speed at the moment of impact is 10.0 $\mathrm{m} / \mathrm{s}$ and decreases to 1.00 $\mathrm{m} / \mathrm{s}$ during a $0.00200-\mathrm{s}$ time interval of contact between the hand and the board. The mass of his hand and arm is $1.00 \mathrm{kg} .$ (b) Estimate the shear stress, assuming this force is exerted on a $1.00-\mathrm{cm}-$ thick pine board that is 10.0 $\mathrm{cm}$ wide. (c) If the maximum shear stress a pine board can support before breaking is $3.60 \times 10^{6} \mathrm{N} / \mathrm{m}^{2},$ will the board break?

Key Concepts

Material Strength and Failure Criteria

This concept refers to the maximum stress that a material can withstand before it fails or breaks. It is a key factor in engineering and physics when determining whether an applied stress, such as shear stress, exceeds the material's capacity to maintain structural integrity, leading to material failure.

Shear Stress

Shear stress is defined as the force per unit area acting parallel to the surface of a material. It is a critical concept in understanding how materials respond to forces that cause layers of the material to slide relative to one another, and it is calculated by dividing the applied force by the cross-sectional area over which the force is distributed.

Impulse-Momentum Theorem

The impulse-momentum theorem states that the impulse on an object, which is the product of the force and the time interval over which it acts, is equal to the change in momentum of the object. This concept allows one to calculate the average force applied during a collision or impact by dividing the object's change in momentum by the duration of the impact.

Force Calculation via Change in Momentum

This concept involves using the relationship F = ?p/?t, where F is the average force acting on an object, ?p is the change in momentum, and ?t is the time interval over which the force acts. It relies on knowing the mass of the object and its change in velocity in order to determine the force applied during an impact or collision.

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