1.  Energy is the capacity of doing work.  Energy methods are useful in analyzing machines that store energy. counterweights springs flywheels Energy Methods Section 8

2. Energy Methods from Newton where: s = displacement v = velocity a = acceleration

3.  Mechanical energy imposed onto an object between two states (locations).  Translating Objects: F s = force in the direction of motion s = displacement Linear Work (U 1  2 )

4. Problem 8-1: A cart is pushed 6 m along the slope by the 300 N force. Determine the work done on the cart. 30 0 300 N 10 0

5.  Mechanical energy imposed onto an object between two states (angles).  Rotating Objects T s = torque about the axis of rotation  = displacement Rotational Work (U 1  2 )

6. Problem 8-8: The flywheel on a punch press delivers 3000 ft-lbs of energy to punch a hole. The flywheel turns two revolutions, for every punch stroke. Determine the average torque that needs to be supplied to the punch press.

7. Potential Energy (PE)  Amount of energy stored in a stationary object.  Potential Energy due to gravity: PE = Wh W = weight of the object h = elevation of the object

8. Problem 8-10: An 1200 lb elevator moves from the 2 nd floor to the 5 th floor, a distance of 36 ft. Determine the increase of potential energy of the elevator.

9. Potential Energy (PE)  Energy Stored in a Spring PE = ½ k x 2 k = spring constant (rate) x = deformation of the spring

10. Problem 8-18: A coil spring is used on a bumper, and has a spring constant of 200 lb/in. Determine the amount of stored energy, as it is compressed the first 3 inches. Also, determine the additional stored energy as it is compressed two additional inches from 3 to 5 inches.

11. Kenetic Energy (KE)  Energy stored in a moving object.  Translating Objects: KE = ½ mv 2 m = mass of the object v = linear velocity of the object

12. Problem 8-20: Determine the kinetic energy of a truck weighing 9000 lbs and traveling at 35 mph. How high would the equivalent amount of energy lift the truck?

13. Kenetic Energy (KE)  Rotating Objects KE = ½ I  2 T s = torque about the axis of rotation  = angular displacement

14. Problem 8-23: Determine the kinetic energy of a 2 m slender rod, with a mass of 10 kg. It is rotated at 20 rpm as shown. 1 m 2 m

15. Conservation of Energy Energy is neither created nor destroyed. It is converted from form to form.  PE +  KE = U 1  2  First Law of Thermodynamics  General Energy Equation

16. Problem 8-26 A dumb waiter and its load have a combined weight of 600 lb. It is configured with an 800 lb counterweight as shown. Determine the energy (work) required from the motor to raise the dumb waiter 12 ft. counterweight dumb waiter

17. Problem 8-30 A lift that is used to dump the contents of a 55 gallon drum is shown below. The maximum density of the contents is12 lbs per gallon. Determine the work required to lift the container 6 ft. The coefficient of friction between the collars and the guide rod is 0.1 6 ft 3 ft

18. Power (P)  Rate of doing work  Units: 1 hp = 550 ft lb/s 1 Nm = 1 Joule (J) 1 Watt (W) = 1 Nm/s = 1 J/s 1 hp = 746 W

19. Power  Translating Objects:  Rotating Objects:

20. Problem 8-34 A belt sander has a belt speed of 400 fpm. The coefficient of friction of new, 100 grit paper is 0.5. Determine the power required to operate the belt when a user presses down with 30 lb while sanding.

21. Problem 8-38 A flexible coupling is rated for 5 hp, when used on a 1200 rpm shaft. Determine the allowable torque for the coupling

22. Problem 8-42 A jack hammer uses a rotary hydraulic motor with a cylindrical cam. The cam has a ramp, which causes the follower to compress a spring, and a step to release the follower. The spring has a rate of 2000 lb/in and the cam lift is 2 in. At the end of the stroke, the spring is compressed 0.5 inches. The hammer weighs 30 lbs. Determine the impact velocity of the hammer. Also, estimate the hydraulic power needed to drive the jackhammer if it delivers 5 strokes per second.

23. Problem 8-42 (con’t) Stationary cam Cam follower Hammer Splined shaft Hydraulic Motor Compression spring Impactor bit

24. Efficiency (  ) Energy conversion is not an ideal process. Some energy is lost with friction and generates heat.

25. Problem 8-49 Crushed stone is being moved from a quarry to a loading dock at a rate of 500 tons/hr. An electric generator is attached to the system in order to maintain constant belt speed. Knowing that the efficiency of the belt/generator system is 70%, determine the average killowatts developed by the generator. The belt speed is 10 ft/sec. 240 ft 3 mi