ME 242 Lecture 19 03.13

# ME 242 Lecture 19 03.13 - P = dW dt = F • v = T • ω...

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1 ME 242 Dynamics March 13, 2009 Eric Wang Today’s Key Concepts Chapter 4: Energy of Particles Potential Energy Example Power Efficiency Example Example (prob. 4.2.28) Given: k=22 N/m and m=55 kg Find: length of bungee cord FBD Which forces are conservative? Don’t double-dip with conservative forces kx mg Before and After Work-Energy Equation

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2 Substitute the givens Check Could we have solved this with Impulse-Momentum? Could we have solved this with F=ma? Concept Quiz A spring loaded Nerf gun is used to shoot a dart straight up in the air. The dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time (ignore friction and assume an ideal spring)? A) 96 m B) 48 m C) 12 m D) 6 m E) 3 m Power & Efficiency Power is the rate of work Mechanical Efficiency P = dW

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Unformatted text preview: P = dW dt = F • v = T • ω power out power in e m = work out work in = Applications Applications 3 Applications Applications For Constant Power If P = constant , can combine with F = ma t 2 − t 1 = 1 P 1 2 mv 2 2 − 1 2 mv 1 2 adx = vdv x 2 − x 1 = 1 P 1 2 mv 2 3 − 1 2 mv 1 3 P = dW dt Example (prob. 4.3.23) • How fast can a 3200 lb car with a 200HP engine accelerate from 0 to 30 mph? (neglect drivetrain losses and air/ road drag) Constant Power Eqn 200 HP = 110,000 ft-lb/s 30 mph = 44 ft/s 3200 lb 99.4 slugs True or False It is possible for power to be negative . 4 Example (prob. 4.3.4) Given: • h = 30 m • e m = 50% • Electricity costs \$.15/kW-hr Find: • Cost to pump 1000 liters Efficiency True or False It is possible for efficiency to be negative . Take Home Points • Power • Mechanical Efficiency e m = P = dW dt = F • v power out power in work out work in =...
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