if a ball was dropped on cement and an identical ball was dropped on stretchy rubber, which scenario would result in the most force acting on the ball?
F=mdv/dt [cement] F'=mdv'/dt' [rubber] then F'/F=(dv'/dv)(dt/dt') if contact time is the same [not true but just as ipothesis] F'/F=(dv'/dv) dv=vi dv'=2vi then F'/F=2 F'=2F in reality the contact time of rubber is significantly higher then cement resulting in an opposite situation F`/F<1 F'<F
The cement. Here's why.... dP = d(mV) = m dV = F dT; where F = ? is the force in question. Note that F = m dV/dT = mV/dT; where V = sqrt(2gh) is the speed of impact for both objects when dropped from h height. So it comes down to dT, the impact interval. dT is the period it takes for the object to come to rest after impact. When that period is short, dt, the force is F = mV/dt and when it's longer, dT > dt, the force is f = mV/dT. So F/f = mV/dt//mV/dT = dT/dt and, ta da: F = f (dT/dt) the force on cement, where the ball comes to an abrupt stop, is (dT/dt) times greater than on the tarp, where the ball takes a bit longer to stop as it is cushioned by the stretching. ANS.
impulse = change in momentum F delta(t) = m delta(v) dropped on cement the ball would essentially lose all its momentum and the time (t) would be very short so F would be high dropped on rubber assuming a good bounce back the change in momentum would be greater because the result would be going back up at some v so impulse is greater but time would also be longer and we would have to know the time it took to bounce on the rubber and the time it took to stop on the cement to make a comparison of forces generally speaking we might reasonably expect the rubber landing to involve less force because we can imagine the difference between jumping from a height onto concrete versus jumping onto a trampoline I would anticipate that the time of contact on the trampoline would be many, many times greater than the time it would take to stop when hitting the concrete. If someone gives you a good response, please consider giving a best answer. This is the only reward we get.
