Work,energy And Power

Work, Energy and Power Power is the time rate of doing work. P=

W P=Fv t

Work is the dot product of force and displacement. W =Fs Energy is the capacity of doing work. 1 KE= m v 2 P E=mgh 2 Units of Work (Energy) Units

Force

Distance

Work

SI

Newton (N)

Meter (m)

Joules (J)

FPS/English

Pound (lbf)

Feet (ft)

ft-lbf

CGS

Dynes (dyn)

Centimeter (cm)

Erg

Note: 1 Btu = 778 ft-lb = 1055Joules = 252 Calories Force Units: 1.0 lbf = 32.2 lbm ft/s2 = 32.2 poundals = 1.0 slug ft/s2 1.0 kgf = 9.81 kgm m/s2 = 9.81 N 1.0 gf 981 gm cm/s2 = 981 dynes Work-Energy Theorem The network done on an object always produces a change in kinetic energy of the object. 1 1 W net =∆ KE ∧∆ KE= m v 12− m v 02 2 2 where: v1 = final velocity v0 = original velocity m = mass of an object

Solved Problem: What is the kinetic energy of a 4000 lb automobile which is moving at 44 ft/sec? 44 ft/sec

Solution: 1 KE= m v 2 2 1 KE= ¿ 2 thus; KE=121000 ft−lb ¿ KE=1.21 x 105 ft −lb

Assignmets 1.) A weight is dropped from a position just above, but not touching, a spring. Show that the maximum deformation produced will be twice that if the same weight is gradually lowered upon string.

2.) A block weighing 96.6 lb is dropped from a height of 4 ft upon a spring whose modulus is 100 1b per in. What velocity will the block have at the instant the spring is deformed 4 in? Ans. 15.3 ft/s 3.) A 600-lb block slides down an incline having a slope of 3 vertical to 4 horizontal. It starts from rest and, after moving 4 ft, strikes a spring whose modulus is 100 lb per feet. If the coefficient of kinetic friction is 0.20, find the maximum velocity of the block. Ans. 12.3 ft/s

4.) A train weighs 1600 tons. The train resistance is constant at 12 lb per ton. If 6000 hp are available to pull this train up a 2% grade, what will be its speed in miles per hour? Ans. 27 mph

5.) A train weighing 1200 tons is pulled up a 2% grade at 10 mph. If the train resistance is constant at 12 lb per ton and the power exerted by the locomotive remains constant, what will be the speed of the train on a level track? What horse-power does the locomotive develop? Ans.

6.) A train weighing 100 tons is being pulled up a 2% grade. The train resistance is constant at 10 lb per ton. The speed of the train is increased from 20 ft per sec to 40 ft per sec in a distance of 1000 ft. Find the maximum horsepower by the locomotive. Ans. 635 hp

7.) Water flows through a nozzle 1 in. in diameter under a head of 400 ft to drive a turbine. The turbine is 90% efficient and is connected to a generator which is 94% efficient. What is the power output in kilowatts? Ans. 25.1 kw

8.) Water enters a hydraulic reaction turbine with a velocity of 12 ft per sec and leaves it 3 ft

lower with a velocity of 4 ft per sec. If 100000 lb of water flow through the turbine each second, compute the horsepower output. Assume the turbine is 80% efficient. Ans. 724 hp