Step 6: Speed testing
Since I earlier made rash claims about shooting ping pong balls at supersonic speed, I need to describe how these speeds were measured.
I made a "ballistic pendulum"; a device once used to measure muzzle velocity of rifle bullets, but now mainly used in physics classes to demonstrate the principles of conservation of momentum and energy. The projectile is shot into a block, and is retained inside the block. The block + projectile then swing due to the momentum of the projectile. The vertical height gain of the block is measured, and when multiplied by the mass of the block + projectile, represents potential energy increase. Using the following equation gives the velocity of the projectile:
Velocity = (m+M)/m (√2gh)
m = mass of projectile, in kilograms (ping pong ball mass = 2.4 g = 0.0024 kg)
M+m = mass of projectile, in kilograms (1.32 kg)
g = acceleration of gravity, 9.81
h = vertical height gain, meters, less height gain from air only tests. (2.5 cm = 0.025 m)
The numbers in parentheses are the average values from my tests.
“A ballistic pendulum is a device for measuring a [projectile's] momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity. Although the ballistic pendulum is considered obsolete, it remained in use for a significant length of time and led to great advances in the science of ballistics. The ballistic pendulum is still found in physics classrooms today, because of its simplicity and usefulness in demonstrating properties of momentum and energy.” (From Wikipedia).
Photos below show the ballistic pendulum I made (along with a view of my screwdrivers and chisels).
The lines on the panel in the background are to measure height, in centimeters.
The laser pointer shows height of the block. In the photos, the first shows height before firing, the second shows maximum height just after firing. A video camera records the action.
The last photo shows the ping pong ball caught in the block.
In addition to momentum from the ball, there is momentum transferred to the block from the air exiting the cannon. I made some test runs using air only and subtracted this average height (0.03 cm) from the tests with ping pong balls.