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

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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

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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

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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?

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

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Example 1…Con’t (High Heels)

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

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Atmospheric Pressure… How Much is it Really? Atmospheric Pressure is measured as 101300N/m 2. Remember what pressure a 60kg woman in high heels applied when stepping on 25cm 2 of you, it was 117600N/m 2. This means that atmospheric pressure is similar to a 60kg woman standing in high heels on every 25cm 2 of your body.

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

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A Very Important Piece

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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?

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

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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.

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

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Let’s Look at this Graphically

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How Pressure is Measured

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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

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Now Who Wants to See it in Action?

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Citations 1.American Journal of Physics, Vol. 72, No. 7, pp. 961–963, July 2004 2.The ballistics of many guns can be found at http://www.volny.cz/buchtik/Revo/Ballisti c_Info_komplet.htm 3.The Physics Teacher, Vol. 43, No. 1, pp. 22–25, January 2005

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D. Roberts PHYS 121 University of Maryland Physic² 121: Phundament°ls of Phy²ics I Friday the 13 th of October, 2006.

D. Roberts PHYS 121 University of Maryland Physic² 121: Phundament°ls of Phy²ics I Friday the 13 th of October, 2006.

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