Energy

Elastic Potential EnergySystemsPower

Varying Forces

Elastic Force, Fs, is Conservative• Force required to stretch/compress spring• Force is _____________ to the amount of

stretching or compression (____________)• Newton’s 3rd Law means the spring exerts an

______ ____ ___________ force• The force is described by Hooke’s Law• It is a ___________ force

15.5kxFs

Potential Energy Stored in a Spring

• The average restoring force exerted by a spring when compressed (or stretched) is:

kxkx

F 21

2

0

xi = 0xf = −x

F1

F0 00 F kxF 1

221 kxxFWs

Elastic Potential Energy• Include work done by spring in work-energy

theorem

gifnc PEKEkxkxW 2212

21

16.5221 kxPEs

17.5sgnc PEPEKEW

Systems and Energy Conservation

• The total amount of energy in the universe remains _________.

• Energy can _______ _____, but it can never be created or destroyed.

• Apply to a ________ of objects that changes from initial state to final state.

• The system may, in general, have energy transferred into or out of it (___________).

Systems

• Wc changes ____

• Rewrite in terms of mechanical energy

• If E changes, it goes somewhere

• For example, friction creates thermal energy

KEWW cnc

ififnc PEPEKEKEW

iiffnc PEKEPEKEW

EEEW ifnc

Nonisolated Systems

Energy is transferred into or out of the system Ways to transfer energy

Work Heat Mechanical Waves Electrical Transmission Electromagnetic Radiation

Power Power is the _____ _____ of energy transfer The energy transfer can change over time Δt so

we use the average power

23.5vFt

xF

t

W

P

Unit is Watt: 1 W = 1 J/s = 1 kgm2/s3

Power

Energy (or work) is sometimes listed in terms of power · time

Electricity usually billed for kilowatt-hours (kWh)

J 1060.3s 3600 W10kWh 1 63

U.S. units are the horsepower (hp)

W746s

lbft550hp 1

Varying Forces• For small displacements x,

Fx nearly __________

• Add up all small rectangles• Work is _____ under graph

xFW x1

321 WWWW

Fig. 5.28, p. 148

For A Spring• Compress or stretch _________

(no heat)• Work is done by applied force• Spring does same work (but it’s

____________)• Change in potential energy is

negative of work done by spring

Fig. 5.29, p. 148

221

appkxWF

appFss WWPE