Force Problem with Punching Glove?

Question

Consider a man with a thick padded punching glove who strikes a bag. He then strikes that same bag without a punching glove. Both punches travel at the same velocity. Which one exerts more force? Which one takes longer to stop?

Here's my understanding:

We know by newton's 2nd law that $F=ma$. With the glove there is more mass and therefore more inertia. So the glove should take longer to stop.

For force, with the glove there is more mass and once again there should be more force.

The answers state that the force with the glove is smaller and the glove takes longer to stop. I seem to have gotten the force one wrong so what did I do incorrectly?

Edit: I understand the correct solution. However I struggle to understand what's wrong with my solution. Why must I neglect the mass?

Answer 1

When you punch someone/something, you're applying an impact force on it and you yourself are experiencing the same force in return (of same megnitude but in opposite direction in accordance with Newton's third law). Consider two different scenarios. You punch the bag, first while wearing the gloves and then without wearing the gloves. In both the cases, suppose you are applying the same impact force. Without the gloves, the momentum change occurs almost instantaneously that is the change in momentum occurs in a very small interval of time. When you are wearing gloves, the change in momentum occurs in a larger interval of time due to the softeness of the glove. Remember that force is equal to change in momentum per unit time interval, so that, whenever the time interval is less the force will be more and vice versa. So the function of the glove is to increase the time interval in which the momentum change is occurring and thereby reducing the magnitude of force that your hand is going to experience. This can be understood using one more example. Suppose you drop a glass utensil on a hard floor. It will break into pieces. But if you drop the same glass utensil on, say a thick cushion or a mattress, it will not break. Because the change in momentum occurs in a very short interval of time when the glass utensil collided with the hard floor but the same change in momentum occurs in a larger interval of time when it fell on a cushion or a mattress. So the force experienced by the utensil is more in case of hard floor, which is why it breaks into pieces.