I suspect the forces may be related in some sort of equal-and-opposite fashion. Or am I misunderstanding the problem?

>The ultimate point that the force on the hand (and thus the force on the ball at moment of impact) is larger than mg is unchanged.

I certainly agree with that point.

>I’m not so sure that his reasoning of the time that it takes for the signal to pass from one side of the ball to the other has “no physical validity”! That seems to be a pretty strong statement for a standard estimation of signal propagation.

I apologize for my provocative language, but I stand by the basic point. (As much as an Anonymous Coward can stand by anything.)

I think everyone agrees that we need to calculate some F=ma equation, and to estimate the acceleration we need an estimate of its duration. It seems to me that what Dr. Mahajan has done to estimate this is to pick a number out of a hat (the speed of sound), but it’s not the relevant number for the problem. The important one is the spring constant of the materials involved, as Tom/swansont pointed out above.*

The spring constant is why if I drop a wine glass on a concrete floor it is more likely to break than if I drop it on a trampoline.

If you’re interested in examples of how to estimate accelerations in a variety of situations, I’d point out that Rhett Allain’s “http://blog.dotphys.net/” blog has a variety of nice examples of calculations of this sort.

*Caveat: accurately working out the problem is more complicated than just the static spring constant due to the fact that we’re looking at dynamics and non-point-objects: at high velocities the mass density of the various objects involved will start to become significant. Working out the crossover between the inertia-dominated regime and the spring-constant-dominated regime is left as an exercise for the reader.

So what is the exact force on the ball? You disagree that the time of impact is on the order of microseconds. I took this calculation directly from Dr. Mahajan, and it was rather an afterthought since the point isn’t the symbolic manipulation. I will do some more thinking on the matter. I’m not so sure that his reasoning of the time that it takes for the signal to pass from one side of the ball to the other has “no physical validity”! That seems to be a pretty strong statement for a standard estimation of signal propagation.

Will think more about this tomorrow, gentle readers.

And check out the video posted by Anonymous, it’s pretty neat.

Even if the rock is infinitely stiff, the hand beneath it isn’t, and will deflect by a few millimeters, not a few microns. This is why one can drop stuff on one’s hand without it shattering.

It’s ironic that an article lamenting the inability of students to use physical reasoning or do order-of-magnitude estimates would use a method of no physical validity to arrive at a numerical answer which is off by orders of magnitude.

P.S. For a fun video of hand vs rock (with the hand deflecting by more than a few millimeters):

Ha! Awesome! ^_^