Force of car at 40mph is equivalent to bowling ball at ?

[denver75]

Hi everyone,
Time for me to do another demonstration for some coworkers, and I want to make sure I'm being accurate.

The idea is to explain how much force a small 2000lb car moving at 40mph has, and then explain the speed that an 8lb bowling ball would need to have the same amount of force.


So far I've been looking at P=mv for the inertia. With that formula I get a velocity of 10,000mph for the bowling ball. That seems excessive!

I'd like to figure this out in terms of impact force, because ultimately we're discussing the damage done in an accident.

Any help on what I might want to look at next?
Thanks!

 

[russ_watters]

Velocity has no force associated with it unless there is an impact and in an impact, the force depends on how much distance or time there is for deceleration. The best you can do to discuss how they behave differently in an impact is with momentum (not inertia), which is mv and/or kinetic energy, which is mv^2.

 

[timmay]

You have three initial variables across the two cases:

- velocity
- energy at impact (function of mass and velocity)
- contact area

The damage done to something that your car and your bowling ball hit will be a function of all three. If you peg both objects' kinetic energy upon impact as the same, the ball will obviously be traveling much faster due to its smaller mass. Depending on the strain rate dependency of the object being impacted, you may find that the faster impact may cause more damage due to a transition from ductile to brittle deformation, or an increase in material stiffness leading to a higher impact force being experienced. In addition, the area over which the kinetic energy is input into the structure will determine damage, as local stresses will be higher the smaller the area.

As Russ says, the best you can consider is the equivalent speed the ball must be traveling at to achieve the same kinetic energy or initial momentum upon impact. Unfortunately it's not an area that can be readily described by equations, but requires a degree of experimentation and/or thought work (as in you know you'd rather be hit by a bowling ball traveling at 30 mph than a car traveling at 30 mph and you can roughly explain why, but you haven't enough information to even begin estimating impact forces or damage).