That's not quite a precise answer to the question.
The change in momentum is the same, but because the
impulse is spread over a greater time, the amount of force acting on your body at any given moment in time is less.
Impulse isn't specific to a single object or to a whole system. It's specific to an
interaction. No force is being exerted before the interaction begins, and no force is being exerted after the interaction ends, and no force is being exerted on other objects in the system that aren't participating in the interaction, but the objects and the system continue to exist both before and after the interaction being considered.
Yes, in physical reality, Δt is never zero -- there's always a span of time involved in a force being applied. If Δt COULD be zero, then a force would have to be
infinite in order to cause any change in momentum.
For the ping-pong ball example, think about watching such an event in slow motion. You would see a period of time after they touch where the balls are deforming around the point of contact, squishing together before bouncing back and returning to their original shape. The more rigid the objects colliding are, the less deformation occurs, and therefore the less time they spend interacting, and therefore the greater the force must be.
That's why hard objects are brittle. They don't readily deform in collisions, so if the force of the impact exceeds the force holding the object together, it breaks.
EDIT:
Quote:
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Is work done so long as there is a net force and is net work done so long as there is a change in velocity?
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No. Work is done as long as there is a net change in position. If the net change in position is zero, you could have exerted all the force you want for as long as you want and you wouldn't have done any work.
There's an argument to be said that work is done if there is a net force, but that's summing up the force vectors over the entire period of time being considered -- in order for the object to end up back where it started, every force applied to it would have needed an opposite force applied to it, and it doesn't matter if those are applied at the same time (meaning no change in velocity) or at different times (meaning velocity changes signs).
... Are you familiar with the difference between scalars and vectors?