The Vacuum Cannon A Penetrating View Into the Physics of Pressure, Force, and Acceleration…

Pressure, Force, and Area Pressure is defined by the equation: P = pressure P = F F = force A A = area The SI units for pressure are Pascals

Pressure, Force, and Area Atmospheric Pressure is Force vs. Pressure: - Force is given by Newton’s 2 nd Law: F=ma - Force tells you how an object will accelerate - Pressure tells you how an object will feel a Force 101.3kPa=101300N/m 2

Example 1 Shaquille O’Neal has a mass of 150kg and wears size 22 shoes, which have an area of approximately 1000cm 2 each. A female with a mass of 60kg wears stilettos with an area of 1cm 2 on each heel and 24 cm 2 on each toe. Calculate the pressure exerted by each person on the ground. Which Shoe would you rather have step on your foot?

Example 1…Con’t (Shaq’s Basketball Shoe)

Example 1…Con’t (High Heels)

Example 1…Con’t So who would you rather have step on your foot? Shaq’s Basketball Shoe : P=7350Pa High Heel : P=117600Pa

Atmospheric Pressure… How Much is it Really? Atmospheric Pressure is measured as N/m 2. Remember what pressure a 60kg woman in high heels applied when stepping on 25cm 2 of you, it was N/m 2. This means that atmospheric pressure is similar to a 60kg woman standing in high heels on every 25cm 2 of your body.

Now Let’s Take a Look at an Application… The Ping-Pong Ball Vacuum Cannon

A Very Important Piece

The First Thought How can we relate Pressure, Force and, Area? What does this give us for Acceleration under constant pressure? What does Newton’s Second Law tell us?

Let’s Do Some Math What muzzle velocity do these equations give us? Is this reasonable?

Let’s Correct This As the ping-pong ball moves along the cannon the air entering not only accelerates the ping-pong ball but the growing column of air behind it. 1 This gives us a new equation for velocity.

This gives us a corrected v(x=1.5m)=241.8m/s

Let’s Look at this Graphically

How Pressure is Measured

A Few Fun Facts from Researchers The E k can be higher than that of a.22 caliber handgun. 2 If He-gas is used to accelerate the ball instead of air velocities as high as 370m/s have been recorded. 3

Now Who Wants to See it in Action?

Citations 1.American Journal of Physics, Vol. 72, No. 7, pp. 961–963, July The ballistics of many guns can be found at c_Info_komplet.htm 3.The Physics Teacher, Vol. 43, No. 1, pp. 22–25, January 2005