Understanding Impulse and Force
When a moving object, like a cricket ball, suddenly changes its direction, it experiences a significant change in momentum. According to Newton's Second Law of Motion, the force applied to an object is directly proportional to the rate of change of momentum.
The Physics Principles
- Momentum ($p$): Defined as the product of mass and velocity ($p = m \cdot v$).
- Impulse ($J$): The change in momentum, given by $J = \Delta p = m(v_f - v_i)$.
- Newton's Second Law: Force is defined as the rate of change of momentum: $F = \frac{\Delta p}{\Delta t} = \frac{m(v_f - v_i)}{\Delta t}$.
Step-by-Step Solution
Given Data:
- Mass ($m$) = $145\text{ g} = 0.145\text{ kg}$
- Initial velocity ($v_i$) = $14\text{ m/s}$ (Let's take this direction as positive)
- Final velocity ($v_f$) = $-22\text{ m/s}$ (Negative because the ball is moving in the opposite direction)
- Time interval ($\Delta t$) = $0.015\text{ s}$
Calculation:
Calculate the Change in Velocity ($\Delta v$): $\Delta v = v_f - v_i = -22\text{ m/s} - 14\text{ m/s} = -36\text{ m/s}$
Calculate the Change in Momentum ($\Delta p$): $\Delta p = m \cdot \Delta v = 0.145\text{ kg} \times (-36\text{ m/s}) = -5.22\text{ kg} \cdot \text{m/s}$
Calculate the Average Force ($F$): $F = \frac{\Delta p}{\Delta t} = \frac{-5.22\text{ kg} \cdot \text{m/s}}{0.015\text{ s}}$ $F = -348\text{ N}$
Intuition
The negative sign indicates that the force acts in the direction opposite to the initial velocity, which is expected since the bat is pushing the ball back toward the bowler. The magnitude of the average force exerted is $348\text{ N}$.