How to Simulate a 15lb Wood 2x4 Impact at 67 mph?

[Moose720]

I posted earlier about testing a project to simulate a wood 2x4 traveling at 67 mph, I did not really get the answers I was looking for so I am going to try to rephase it. My project needs to withstand the impact of a 15lb wood 2x4 traveling at 67 mph. I want to simulate this test but in a vertical fashion. I can set up a drop test up to the height of 15ft. My main question is, how much weight needs to be added to the 15lb wood 2x4 to achieve the same impact as the 15lb 2x4 @ 67mph, and also what height would it needed to be dropped from. Air resistance not a concern for this test. What formulas are used to get the results?

 

[Moose720]

When I say impact, I mean just before the 2x4 would strike the surface.

 

[Moose720]

Or am I looking for Kinetic Energy??

 

[zts1986]

Moose, this is how I would go about it:

1. Figure out how fast the object is moving when dropped from 15 feet. This can be done with the known acceleration due to gravity (32.2 ft/s^2). This is the average acceleration across the Earth's surface. If you wanted a more accurate number, you'd have to factor in your elevation. This won't be necessary or matter for this purpose, unless you're at the summit of Mt. Everest or something. Anyway, the formula for the velocity of a free-falling object on Earth given a certain height is as follows:
v = sqrt(2*g*d)
v = sqrt (2 * 32.2 ft/s^2 * 15 ft)
v = 31.08 ft/s = 21.19 mph

2. Given the velocity of the object in your experiment, the desired velocity, and the desired weight, you can set up an equation of momentum. The main principle here is that you desire a momentum produced by a 15 lb object going 67 mph. Momentum is equal to the product of mass and velocity (p = m*v). Since you're looking to recreate the momentum from the desired experiment and you cannot change the velocity, you have to add mass. That gives you the following equation:
m1v1 = m2v2
(15 lb)*(67 mph) = (X lb)*(21.19 mph)
X = 47.43 lbs

3. So, for your experiment to produce the required momentum, your total weight needs to be 47.43 ~ 47.5 pounds. You currently have a 15 lb mass so therefore, you need to add an extra 32.5 lbs of mass to your weight.

4. Just as a note, there are some inaccuracies in this experiment. The calculations I made were using point-masses, not actual objects. The difference is not very large at all and will be negligable in what you're trying to accomplish. I would not worry about those. I figure that if air resistance isn't necessary, then it isn't necessary to dive into the center of mass/inertia values for the mass.

Hope this helps!