Work, Energy & Power

ENERGY IS CONSERVED

• The law of conservation of mechanical energy states: Energy cannot be created or destroyed, only transformed!

• Energy Before

• Energy After

• Am I moving? If yes,
• KEo
• Am I above the ground? If yes, PEo

• Am I moving? If yes,
• KE
• Am I above the ground? If yes, PE

Energy consistently changes forms

Energy consistently changes forms

Position	m	v	U	K	ME
1	60 kg	8 m/s

• Am I above the ground?
• Am I moving?

• NO, h = 0, U = 0 J

• 0 J

• Yes, v = 8 m/s, m = 60 kg

• 1920 J

• (= U+K)

• 1920 J

Energy consistently changes forms

Position	m	v	U	K	ME
1	60 kg	8 m/s	0 J	1920 J	1920 J
2	60 kg

• Energy Before

• = Energy After

• KO

• = U + K

• = (60)(9.8)(1) + (.5)(60)v2
• 1920= 588 + 30v2

• 588 J

• = 30v2
• 44.4 = v2
• v = 6.66 m/s

• 6.66 m/s

• 1920 J

• 1332 J

Energy consistently changes forms

Position	m	v	U	K	ME
1	60 kg	8 m/s	0 J	1920 J	1920 J
2	60 kg	6.66 m/s	588 J	1332 J	1920 J
3	60 kg				1920 J

• Am I moving at the top?

• No, v = 0 m/s

• 0 m/s

• 0 J

• 1920 J

• EB = EA

• Using position 1
• Ko = U
• = mgh
• 1920 =(60)(9.8)h
• h = 3.27 m

Example

• A 2.0 m pendulum is released from rest when the support string is at an angle of 25 degrees with the vertical. What is the speed of the bob at the bottom of the string?

• L

• 

• Lcos

• h

• h = L – Lcos
• h = 2-2cos
• h = 0.187 m

• EB = EA

• UO = K
• mgho = 1/2mv2
• gho = 1/2v2
• 2(1.83) = v2
• 1.94 m/s = v

Springs – Hooke’s Law

• Hooke's Law describes the force needed to stretch an elastic object. This is primarily in reference to SPRINGS.

• The negative sign only tells us that “F” is what is called a RESTORING FORCE, in that it works in the OPPOSITE direction of the displacement.

Hooke’s Law

• Common formulas which are set equal to Hooke's law are N.S.L. and weight

Example

• A load of 50 N attached to a spring hanging vertically stretches the spring 5.0 cm. The spring is now placed horizontally on a table and stretched 11.0 cm. What force is required to stretch the spring this amount?

• 1000 N/m

• 110 N

Hooke’s Law from a Graphical Point of View

x(m)	Force(N)
0	0
0.1	12
0.2	24
0.3	36
0.4	48
0.5	60
0.6	72

• Suppose we had the following data:

• k =120 N/m

We have seen F vs. x Before!!!!

• Work or ENERGY = Fx
• Since WORK or ENERGY is the AREA, we must get some type of energy when we compress or elongate the spring. This energy is the AREA under the line!

• Area = ELASTIC POTENTIAL ENERGY

• Since we STORE energy when the spring is compressed and elongated it classifies itself as a “type” of POTENTIAL ENERGY, Us. In this case, it is called ELASTIC POTENTIAL ENERGY (EPE).

Elastic Potential Energy

• The graph of F vs.x for a spring that is IDEAL in nature will always produce a line with a positive linear slope. Thus the area under the line will always be represented as a triangle.

• NOTE: Keep in mind that this can be applied to WORK or can be conserved with any other type of energy.

Conservation of Energy in Springs

Example

• A slingshot consists of a light leather cup, containing a stone, that is pulled back against 2 rubber bands. It takes a force of 30 N to stretch the bands 1.0 cm (a) What is the potential energy stored in the bands when a 50.0 g stone is placed in the cup and pulled back 0.20 m from the equilibrium position? (b) With what speed does it leave the slingshot?

• 3000 N/m

• 300 J

• 109.54 m/s

Power

• One useful application of Energy is to determine the RATE at which we store or use it. We call this application POWER!
• As we use this new application, we have to keep in mind all the different kinds of substitutions we can make.
• Unit = WATT or Horsepower