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Chapter 7: Problem 18

When hit in the face, a boxer will "ride the punch"; that is, if he anticipates the punch, he will allow his neck muscles to go slack. His head then moves back easily from the blow. From a momentum-impulse standpoint, explain why this is much better than stiffening his neck muscles and bracing himself against the punch.

Short Answer

Expert verified
Answer: Riding the punch is better from a momentum-impulse standpoint because it increases the time interval over which the impulse is applied, resulting in a lower force experienced by the boxer's head and neck, reducing the risk of injury.

Step by step solution

01

Define momentum and impulse

Momentum (p) is the product of an object's mass (m) and its velocity (v), and is given by the equation p = mv. Impulse (J) is the product of force (F) and the time interval (∆t) over which the force is applied, and is given by the equation J = F∆t. In any collision, the total momentum is conserved. Impulse is the change in momentum experienced by an object (∆p).
02

Describe the two scenarios

In this exercise, we will consider two scenarios: A) Boxer "rides the punch" by allowing their neck muscles to go slack and their head to move back easily. B) Boxer stiffens their neck muscles and braces against the punch. In both cases, the input force from the punch and the time it takes to transfer the momentum remain the same.
03

Compare the momentum and impulse for the two scenarios

Since the total momentum is conserved, the impulse, which is the change in momentum experienced by the boxer, will be the same in both scenarios. However, the time interval (∆t) during which the impulse is applied will be different. In scenario A (riding the punch), the time interval will be longer due to the head moving back easily. In scenario B (bracing), the time interval will be shorter as the head remains relatively still upon impact.
04

Calculate the force experienced by the boxer

By calculating the force experienced by the boxer in both scenarios, we can determine which is better from a momentum-impulse standpoint. Using the equation for impulse (J = F∆t) and keeping in mind that impulse is the same in both scenarios, we get: In scenario A: F1 * ∆t1 = J In scenario B: F2 * ∆t2 = J Since ∆t1 > ∆t2 (riding the punch results in a longer time interval), F1 will be less than F2. This means that the force experienced by the boxer when riding the punch (F1) is less than that experienced when bracing against the punch (F2).
05

Conclusion

From a momentum-impulse standpoint, riding the punch by allowing the neck muscles to go slack and the head to move back easily is better than stiffening the neck muscles and bracing against the punch. This is because the longer time interval over which the impulse is applied results in a lower force experienced by the boxer's head and neck, reducing the risk of injury.

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