Energy is the capacity of

1
Energy Methods
Section 8

• Energy is the capacity of
• doing work.
• Energy methods are useful in analyzing machines
  that store energy.
• counterweights
• springs
• flywheels

2
Energy Methods from Newton
where s displacement v velocity a
acceleration
3
Linear Work (U1?2)

• Mechanical energy imposed onto an object between
  two states (locations).
• Translating Objects
• Fs force in the direction of motion
• s displacement

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.

300
300 N
100
5
Rotational Work (U1?2)

• Mechanical energy imposed onto an object between
  two states (angles).
• Rotating Objects
• Ts torque about the axis of rotation
• Dq displacement

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 2nd floor to
  the 5th 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 x2
• 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 mv2
• 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 Iw2
• Ts torque about the axis of rotation
• Dq 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.

15
Conservation of Energy

• Energy is neither created nor destroyed. It is
  converted from form to form.
• DPE DKE U1?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.

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

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 (cont)
24
Efficiency (h)

• 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.