Jim Watson said:
The primer sensitivity test used in the WW II era was as follows:
30 cal (.30-06)
A 4 oz ball dropped 15 inches on a firing pin in a test fixture must fire all rounds.
A 4 oz ball dropped 3 inches must not fire any.
Takes a little math to get the force or energy in scientific units, that is left as an exercise for the student.
Well, I took a Kinetics and Motion course last semester so I can help out with this.
First, realize that you can't talk about this in terms of force. Why? Because Force = mass*acceleration, and for both situations, mass and acceleration are the same, so the amount of force being applied is the same.
What we can talk about is energy, because that's different for each case. First let's convert our units to SI units so they're easier to work with. 4 oz = 0.1134 kg, 15 in = 0.381 m, and the acceleration of gravity is ~9.8 m/s^2.
The first equation we'll use is height = (initial velocity)(time) + (1/2)(acceleration)(time)^2. This equation is useful because our initial velocity is 0, since the ball is being held and dropped (presumably from someone's hand). Thus, the first term of this equation cancels out and we're left with h=(1/2)(a)(t^2). Plug in .381m for h, 9.8 m/s^2 for a, and solve for t. Doing this gives a value of 0.2788 s, which is the time required for the ball to impact the firing pin.
Now we need to figure out the final velocity of the ball at the instant before it hits the firing pin. For this we'll use velocity=(acceleration)(time)+(initial velocity). Again, the initial velocity term drops out and we're left with v=at. Plug in 9.8 m/s^2 for a and our value of 0.2788 s for t. This gives us a value of 2.73 m/s for our final velocity.
Finally we're getting somewhere. Using the equation Kinetic Energy=(1/2)(mass)(velocity^2), we can plug in our mass (0.1134 kg) and our final velocity (2.73 m/s).
This gives us a value of 0.423 J, which is the amount of energy generated in the situation provided for us by Jim Watson.