Question

question 6. during training, a boxer is using a force sensor attached to the punching bag. if the boxer chooses to wear heavy padded gloves, what is a design performance issue that the gloves can exhibit? assume that the boxer has a constant punching velocity regardless of which gloves are worn. select two correct answers. a. the heavier gloves cause a decreased force on the bag because the mass increases the momentum of the gloves. b. the padding in the gloves causes a decreased force on the bag because the cushion increases the time interval of the impact. c. the padding in the gloves causes an increased force on the bag because the cushion decreases the time interval of the impact. d. the heavier gloves cause an increased force on the bag because the mass increases the momentum of the gloves. e. the heavy, padded gloves decrease the force on the bag because the momentum and average force are increased due to the increased time interval of the impact.

Explanation:

Step1: Analyze the relationship between momentum, force, and time interval

According to the impulse - momentum theorem, \(J = F\Delta t=\Delta p\). Here, \(\Delta p\) is the change in momentum of the punching bag (assuming the bag is initially at rest and comes to rest after the impact, \(\Delta p = p - 0\), where \(p = mv\) for the boxer's fist - glove system). If the boxer has a constant punching velocity, the mass of the gloves \(m\) affects the momentum \(p = mv\). Heavier gloves mean a larger mass \(m\), so a larger momentum \(p\) (since \(v\) is constant), which can cause an increased force on the bag (if the time interval \(\Delta t\) is the same). But when considering padding: Padding increases the time interval \(\Delta t\) of the impact. From \(F=\frac{\Delta p}{\Delta t}\), if \(\Delta p\) (related to the boxer's motion, assume the boxer's own motion - related momentum transfer to the bag is somewhat fixed in terms of the "punching effort" in a sense, here we focus on the effect of gloves). For the padding part, more padding (heavier padded gloves) increases the time interval \(\Delta t\) of the impact. If \(\Delta p\) (the impulse that the boxer imparts to the bag, related to the boxer's movement before and after the punch) is considered (assuming the boxer's "punching action" leads to a certain \(\Delta p\) on the bag), then \(F=\frac{\Delta p}{\Delta t}\). An increase in \(\Delta t\) (due to padding) will decrease the force \(F\) on the bag.

Step2: Evaluate each option

- **Option A**: Heavier gloves (\(m\) increases) with constant velocity \(v\) (from the problem statement: "constant punching velocity"), so \(p = mv\) increases. But this is not about the force - time - momentum relationship in terms of the impact time. The formula \(F=\frac{\Delta p}{\Delta t}\), if \(\Delta t\) is not considered in this option's reasoning (it just says mass increases momentum, but doesn't relate to force on the bag correctly as per the impulse - momentum theorem considering impact time), so this option is incorrect.
- **Option B**: Padding increases the time interval \(\Delta t\) of the impact. Using \(F = \frac{\Delta p}{\Delta t}\) (assuming \(\Delta p\) is related to the boxer's punching action, a relatively fixed quantity for a given "punching effort" in terms of the transfer to the bag), an increase in \(\Delta t\) leads to a decrease in \(F\) (force on the bag). This option is correct.
- **Option C**: Padding increases \(\Delta t\), so from \(F=\frac{\Delta p}{\Delta t}\), force \(F\) should decrease, not increase. This option is incorrect.
- **Option D**: Heavier gloves (mass \(m\) increases) with constant \(v\) gives \(p=mv\) increases. But if we consider the force on the bag \(F=\frac{\Delta p}{\Delta t}\), if we assume that the "punching action" (the way the boxer moves to punch) gives a certain \(\Delta p\) (the impulse transferred to the bag), and if we only consider the mass of the gloves increasing momentum (but not considering the impact time, which is a key factor in the force - momentum relationship \(F=\frac{\Delta p}{\Delta t}\)), this option is incorrect.
- **Option E**: Heavier padded gloves: Padding increases \(\Delta t\). From \(F=\frac{\Delta p}{\Delta t}\), if \(\Delta p\) (related to the boxer's punching action's impulse transfer to the bag) is considered, an increase in \(\Delta t\) leads to a decrease in \(F\). Also, if we consider the momentum of the gloves - fist system, but the main relationship for force on the bag is through \(F=\frac{\Delta p}{\Delta t}\) with \(\Delta t\) increase (due to padding). Mass of gloves (for momentum) is not the main factor here as the problem is about the design issue (padding). This option is incorrect.

Answer:

B. The padding in the gloves causes a decreased force on the bag because the cushion increases the time interval of the impact.