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EE 255 - Chapter 1a

# EE 255 - Chapter 1a - Chapter 1 Introduction to Machinery...

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1 Chapter 1 : Introduction to Machinery Principles 1-1. A motor’s shaft is spinning at a speed of 3000 r/min. What is the shaft speed in radians per second? S OLUTION The speed in radians per second is ( ) 1 min 2 rad 3000 r/min 314.2 rad/s 60 s 1 r π ω g167 g183g167 g183 = = g168 g184g168 g184 g169 g185g169 g185 1-2. A flywheel with a moment of inertia of 2 kg m 2 is initially at rest. If a torque of 5 N m (counterclockwise) is suddenly applied to the flywheel, what will be the speed of the flywheel after 5 s? Express that speed in both radians per second and revolutions per minute. S OLUTION The speed in radians per second is: ( ) 2 5 N m 5 s 12.5 rad/s 2 kg m t t J τ ω α g167 g183 = = = = g168 g184 g169 g185 The speed in revolutions per minute is: ( ) 1 r 60 s 12.5 rad/s 119.4 r/min 2 rad 1 min n π g167 g183g167 g183 = = g168 g184g168 g184 g169 g185g169 g185 1-3. A force of 5 N is applied to a cylinder, as shown in Figure P1-1. What are the magnitude and direction of the torque produced on the cylinder? What is the angular acceleration α of the cylinder? S OLUTION The magnitude and the direction of the torque on this cylinder is: CCW , sin ind θ τ rF = ( )( ) ind 0.25 m 10 N sin 30 1.25 N m, CCW τ = ° = The resulting angular acceleration is: 2 2 1.25 N m 0.25 rad/s 5 kg m J τ α = = = 1-4. A motor is supplying 60 N m of torque to its load. If the motor’s shaft is turning at 1800 r/min, what is the mechanical power supplied to the load in watts? In horsepower? S OLUTION The mechanical power supplied to the load is ( )( ) 1 min 2 rad 60 N m 1800 r/min 11,310 W 60 s 1 r P π τω = = =

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2 ( ) 1 hp 11,310 W 15.2 hp 746 W P = = 1-5. A ferromagnetic core is shown in Figure P1-2. The depth of the core is 5 cm. The other dimensions of the core are as shown in the figure. Find the value of the current that will produce a flux of 0.005 Wb. With this current, what is the flux density at the top of the core? What is the flux density at the right side of the core? Assume that the relative permeability of the core is 1000. S OLUTION There are three regions in this core. The top and bottom form one region, the left side forms a second region, and the right side forms a third region. If we assume that the mean path length of the flux is in the center of each leg of the core, and if we ignore spreading at the corners of the core, then the path lengths are 1 l = 2(27.5 cm) = 55 cm, 2 l = 30 cm, and 3 l = 30 cm.
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EE 255 - Chapter 1a - Chapter 1 Introduction to Machinery...

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