4a._Fundamentals_of_Mechanics_2011

4a._Fundamentals_of_Mechanics_2011 - Fundamentals of...

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EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics 1 Fundamentals of Mechanics and Electromechanical Energy Conversion (Not explicitly covered in the Chapman text.) Revised 5/11/11 8:53 AM

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EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics 2 Mechanical Work and Power Mechanical work is force acting over a distance. W = Fd W : Work [Joules] F : Force [Newtons] d : distance the force moves [meters] Power is the rate of doing work P = W/T P : Power [Watts] T : Time [seconds]
EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics 3 Mechanical Work and Power If a motor lifts a mass of 500 kg to a height of 30 m in 12 s, then the power developed by the motor is F = mg * = 9.8 ! 500 = 4900 N W = Fd = 4900 ! 30 = 147,000 J P = W / T = 147,000 /12 = 12,250 W = 12,250 / 746 = 16.4 hp 1 hp = 746 w ( ) * F gravity = 9.8 ! mass

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EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics 4 Power of a Motor Linear motion Rotational motion v : linear velocity [m/s] τ : Torque [Nm] ω m : Motor speed in radians/second n m : Motor speed in revolutions/minute Note the conversion: 30 9.55 mm m PF v nn P ττ ωτ π = == = ! m rad sec " # \$ % & ' = n m rpm ( ) ( 1 60 min sec " # \$ % & ' ( 2 ) rad rev " # \$ % & ' = 30 n m = n m 9.55
EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics 5 Kinetic Energy – Energy due to motion For linear motion: For rotational motion: v : linear velocity [m/s] J : Moment of Inertia [kg . m 2 ] J, is the moment of inertia or simply the inertia, and depends on the shape of the mass. 2 1 2 k Em v = E k = 1 2 J ! 2 = 5.48 " 10 # 3 J i n 2

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EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics 6 Moment of Inertia of Common Shapes 2 Jm r = 2 2 m Jr = ( ) 22 12 2 m JR R =+ 2 12 m JL = ( ) 121 2 3 m R R R +
EEL 3211 (© 2011 H. Zmuda) 4a. Fundamentals of Mechanics

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This note was uploaded on 08/23/2011 for the course EEL 3211 taught by Professor Staff during the Summer '08 term at University of Florida.

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4a._Fundamentals_of_Mechanics_2011 - Fundamentals of...

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