In last week’s recitation question (scroll down two posts if you don’t know what I’m talking about), we examined a bullet (mass m) hitting a block (mass M) hanging from a string (length L). At the end I ask you what would have happened if there was an inelastic collision and the bullet was stuck in the block. Can you find it’s initial velocity now? I encourage you to go back and try this problem if you haven’t already. You should be able to use conservation of energy to get v_i=[1+(m/M)]√2gh, where h is how high the pendulum swung.

Find the initial velocity based on the height which the pendulum reached.

You might be asking yourself, why do we care? Why am I solving this problem? Will this ever matter to anyone?

YES. We did not invent this problem out of thin air, this problem comes from an actual device.

The “ballistic pendulum” was invented in 1742 as a device for testing the firepower of military weapons. If you are about to mass produce 500,000 muskets for your growing empire, you will probably want to know some quantitative numbers about the weapons you’re producing. This is a time before high-speed cameras, before radar-guns, and before precise clocks – how else would you go about trying to accurately measure the speed of a bullet?

An actual ballistic pendulum.

This problem is especially important when it comes to knowing the velocity of artillery shells. When we solve a 2D projectile motion problem, we call it a “cannon problem.” The techniques to solve this problem were developed by real people needed to shoot real cannons at real targets – often shooting over the heads of their own comrades. How confident do you feel about solving a cannon problem on an exam? How confident do you think you would feel solving the same question, while under enemy fire, knowing that you are about to destroy an area the size of a football field? You’d probably feel more confident if you knew that the initial velocity was measured accurately, which is exactly why they invented the ballistic pendulum.