User:Kbh3rd/Joules

Electrical energy in the capacitors
A bank of five identical 300 volt 80μF capacitors in parallel was used. The energy stored in a capacitor is given by:


 * $$E=\frac{1}{2} U^2 C$$

Where:
 * E = Energy in capacitor in joules (j)
 * U = Voltage in capacitor in volts (v)
 * C = Capacitor capacitance in farads (F)

The bank of five 80μF capacitors have a combined capacitance of 400μF, which is 0.0004F. So the energy in the bank of capacitors when charged to capacity at 300v, in joules, is:


 * $${ (300 \mathrm{v})^2 \cdot 0.0004 \mathrm{F} \over 2} = { 90000v^2 \cdot 0.0004 \mathrm{F} \over 2 } = 18 \mathrm{j}$$

Note: The charge in the capacitors was not measured; it is likely that the boost circuit did not charge to a full 300v.

Volume of spherical projectile
Diameter = ¼ inch = 0.635 cm; radius = 0.3175 cm Volume of a sphere given by: $$\frac{4}{3} \pi r^3$$ The volume of the projectile is 0.134066 cm3

Mass of projectile
No small scale was available, so the average value for the density of mild steel was used: 7.85 g/cm3 Therefore, the mass of the projectile is calculated to be 1.052421g or 0.001052421kg

Velocity of projectile
The projectile was recorded exiting the coil on digital video shot at 29.412 frames/second. The distance that the projectile travelled between 2 successive frames was estimated at 14cm. That gives a velocity of 4.11768 m/s.

''Note: The video frames used are of the projectile some distance after it exited the coil, and include a shallow bounce off a hard floor; it is very likely that the maximum velocity was greater than what could be measured. Also, the exact distance travelled between frames could not be measured, but was estimated using the patterned floor in the background of the shot: The value for the velocity given here is an estimate and likely less than maximum achieved.''

Kinetic energy
The kinetic energy of a mass in motion, measured in joules, is given by:
 * $$E_k = \frac{1}{2} M V^2$$

where M is mass in kilograms, and V is velocity in meters per second. With the values for the mass and velocity of the projectile, that gives a kinetic energy of 0.004760 j.

Efficiency of energy converstion
Maximum stored electrical energy: 18 j Estimated kinetic energy: 0.00476 j Estimated minimum conversion efficiency: 0.0264%