Question

Estimate the force with which a karate master strike a board, assuming the hand’s speed at the moment of Impact is $ 10.0m{s^{ - 1}} $ , decreasing to $ 1.00m{s^{ - 1}} $ during a $ 0.002s $ time internal of contact between the hand and the board. The mass of his hand and arm is $ 1.00kg $

Answer 1

Hint: we will use the concept of impulse-momentum theorem which states that for an object the change in momentum will be equal to the impulse applied. This will give us the relation between the force applied for a duration of time, velocity, and mass. Using this relation we will find the force with which a karate master strikes a board.
 $ Ft = mv $
Where, $ F $ is the force applied, $ t $ denotes time, $ m $ is the mass of the body , $ v $ is the speed of impact.

Complete Step By Step Answer:
momentum of an object is the product of mass and velocity. It tells us the measurement of mass in motion.
 $ \rho = mv $ where $ m $ is the mass of the body , $ v $ is the speed of the body.
For change of momentum we write $ \Delta \rho = m\Delta v $ where $ \Delta v $ is change in speed.
Impulse is the quantity of the total force acting on a body in a period of time.
 $ J = F\Delta t $ where $ F $ is the force applied, $ t $ is the time.
We can create a direct relationship between how a force operates on an object over time and the object's motion according to the impulse-momentum theorem.
 $ Ft = m\left( {{v_f} - {v_i}} \right) $ where $ {v_f} $ and $ {v_i} $ are the final and initial velocities.
 $ \Rightarrow F\left( {0.002s} \right) = \left( {1.00kg} \right)\left( {1.00m{s^{ - 1}} - 10.0m{s^{ - 1}}} \right) $
 $ \Rightarrow F = - 4500N $
Hence, the force with which a karate master strikes a board is $ F = 4500N $ .

Note:
The impulse-momentum theorem is equivalent to Newton's second law of motion.
According to the impulse-momentum theorem $ J = \Delta \rho $
For constant mass $ F\Delta t = m\Delta v $
For variable mass $ Fdt = vdv + vdm $
SI unit of impulse is $ Newton\sec $
SI unit of momentum is $ \dfrac{{kg\left( {meter} \right)}}{{\sec }} $