Question

1. write the equation for the impulse - momentum theorem and define all the variables.
2. what is the si unit for impulse?
3. professional boxers wear 8 oz. or 10 oz. gloves depending on the weight class. with the impulse - momentum theorem in mind, describe why boxers use gloves for the safety of themselves and their opponents. use complete sentences to receive full credit.

Explanation:

Question 3

The Impulse - Momentum Theorem states that the impulse (\(J\)) applied to an object is equal to the change in its momentum (\(\Delta p\)). The equation is \(J=\Delta p\).

Impulse (\(J\)) is calculated as \(J = F\Delta t\), where \(F\) is the average force applied and \(\Delta t\) is the time interval over which the force is applied.

Momentum (\(p\)) is given by \(p = mv\), where \(m\) is the mass of the object and \(v\) is its velocity. So, \(\Delta p=p_{f}-p_{i}=m(v_{f} - v_{i})\), where \(p_{i}\) and \(p_{f}\) are the initial and final momenta, and \(v_{i}\) and \(v_{f}\) are the initial and final velocities respectively.

Since \(J = F\Delta t\), and the SI unit of force (\(F\)) is the Newton (\(N\)) and the SI unit of time (\(\Delta t\)) is the second (\(s\)). So, the SI unit of impulse (\(J\)) is \(N\cdot s\). Also, since \(J=\Delta p\) and \(p = mv\) (\(m\) in \(kg\) and \(v\) in \(m/s\)), \(p\) has units \(kg\cdot m/s\). And \(1N = 1kg\cdot m/s^{2}\), so \(N\cdot s=(kg\cdot m/s^{2})\cdot s=kg\cdot m/s\)

According to the impulse - momentum theorem \(J = F\Delta t=\Delta p\). When a boxer throws a punch, the change in momentum (\(\Delta p\)) of the boxer's hand (and ultimately on the opponent) is relatively fixed (based on the motion of the boxer's arm). Gloves increase the time of contact (\(\Delta t\)) between the boxer's hand and the opponent (or the punching bag). From \(F=\frac{J}{\Delta t}\), if \(J\) (impulse, related to \(\Delta p\)) is constant, increasing \(\Delta t\) (by wearing gloves) decreases the force (\(F\)). A lower force reduces the risk of injury to both the boxer (by reducing the force on their hand bones) and the opponent (by reducing the force of impact on the opponent's body).

Answer:

The equation for the Impulse - Momentum Theorem is \(J=\Delta p\), where \(J\) (impulse) \(=F\Delta t\) (\(F\): average force, \(\Delta t\): time interval), and \(\Delta p\) (change in momentum) \(=m(v_{f}-v_{i})\) (\(m\): mass, \(v_{i}\): initial velocity, \(v_{f}\): final velocity)

Question 4