Hypothetical

[chiyo_no_saru]

Someone is Wrong on the Internet, and I can't figure out the math myself. (It's not for homework or anything, just to prove a point.)

How hard/how fast would you have to hit a 100lb weight with a 7lb bat to lift it off the ground? Assume no shock absorption, air resistance, etc.

Comments

[just_you_wait]

To get the weight off the ground, you need to supply over 100lbs of upwards force, regardless of the mass or speed of the bat. I could hook the bat to the weight and lift the weight by the bat as slow as I wanted.

If you want to treat this as a collision problem, you'll need to make assumptions about, or treat as variables, the coefficient of restitution and the impact time.
If we assume C_R=1 (elastic collision), then after some algebra, the bat's upward velocity (ft/s) must be ~246x the impact time (s).
If we assume C_R=0 (perfectly inelastic), then the bat's upward velocity (ft/s) must be ~492x the impact time (s).

So if we estimate v=300t (figure C_R is closer to 1, and not wanting to make further calculations) and t=0.05s (seems plausible?), a ballpark estimate might be that the bat's speed needs a 15 ft/s vertical component, hopefully within an order of magnitude. That assumes the upward force component runs through the center of mass of the weight (i.e. is not an oblique hit).