Chapter 07: Kinetic Energy and Work Like other undamental concepts, energy is harder to deine in words than in equations. It is closely linked to the concept o orce. Conservation o Energy is one o Nature s undamental laws that is not violated. Energy can take on dierent orms in a given system.
Forms o energy Kinetic energy: the energy associated with motion. Potential energy: the energy associated with position or state. (Chapter 08) Heat: thermodynamic quanitity related to entropy. Conservation o Energy is one o Nature s undamental laws that is not violated. That means the grand total o all orms o energy in a given system is (and was, and will be) a constant.
Dierent orms o energy Kinetic Energy: linear motion rotational motion Potential Energy: gravitational spring compression/tension electrostatic/magnetostatic chemical, nuclear, etc... Mechanical Energy is the sum o Kinetic energy + Potential energy. (reversible process) Friction will convert mechanical energy to heat. Basically, this (conversion o mechanical energy to heat energy) is a non-reversible process.
Chapter 07: Kinetic Energy and Work Kinetic Energy is the energy associated with the motion o an object K = (1/) mv m: mass and v: speed This orm o K.E. holds only or speeds v << c. SI unit o energy: 1 joule = 1 J = 1 kg.m /s Other useul unit o energy is the electron volt (ev) 1 ev = 1.60 10-19 J
Work Work is energy transerred to or rom an object by means o a orce acting on the object Work done by a constant orce: W = ( F cos φ) d = F d cos φ In general, W v = F ds v
Work done by a constant orce: W = F d cos φ = F. d when φ < 90 o, W positive when φ > 90 o, W negative when φ = 90 o, W = 0 When F or d is zero, W = 0 Work done on the object by the orce Positive work: object receives energy Negative work: object loses energy
W = F d cosφ = F. d SI Unit or Work 1 N. m = 1 kg. m/s. m = 1 kg. m /s = 1 J Net work done by several orces Σ W = F net. d = ( F 1 + F + F 3 ). d = F 1. d + F. d + F 3. d = W 1 + W + W 3
Work-Kinetic Energy Theorem The change in the kinetic energy o a particle is equal the net work done on the particle K = K K... or in other words, i = W net = 1 mv 1 mv inal kinetic energy = initial kinetic energy + net work 1 1 K = mv = Ki + Wnet = mvi + i W net
A particle moves along the -ais. Does the kinetic energy o the particle increase, decrease, or remain the same i the particle s velocity changes: (a) rom 3 m/s to m/s? (b) rom m/s to m/s? (c) In each situation, is the work done positive, negative or zero?
Work done by Gravitation Force W g = mg d cos φ throw a ball upwards: during the rise, W g = mg d cos180 o = mgd negative work, K, v decrease mg d during the all, W g = mgd cos0 o = mgd positive work, K, v increase mg d
Work done by an applied orce in liting and lowering an object: In the special case that the object is stationary both beore and ater the lit v i = v = 0 then K i = K = 0 K K i = W net = W a + W g so W a + W g = 0 => W a = W g = mg d cos φ
Sample problem 7-5: An initially stationary 15.0 kg crate is pulled a distance L = 5.70 m up a rictionless ramp, to a height H o.5 m, where it stops. (a) How much work W g is done on the crate by the gravitational orce F g during the lit?
How much work W t is done on the crate by the orce T rom the cable during the lit?
Work done by a variable orce Three dimensional analysis = Σ = = Σ = Σ = i avg j avg j j avg j j d F W F F W W F W ) ( lim, 0,, F dz dy F F d W i i i z z z y y y + + =
Work done by a spring orce The spring orce is given by F = k ( Hooke s law) k: spring (or orce) constant k relates to stiness o spring; unit or k: N/m. Spring orce is a variable orce. = 0 at the ree end o the relaed spring.
Work done by a spring orce The spring orce tries to restore the system to its equilibrium state (position). Eamples: springs molecules pendulum Motion results in Simple Harmonic Motion
Work done by Spring Force Work done by the spring orce W s = Fd = i i ( k)d I > i (urther away rom = 0); W < 0 k I < i (closer to = 0); W > 0 = 1 i 1 k I i = 0, = then W s = ½ k
The work done by an applied orce. I the block is stationary both beore and ater the displacement: v i = v = 0 then K i = K = 0 work-kinetic energy theirem: W a + W s = K = 0 thereore: W a = W s
Power The time rate at which work is done by a orce Average power P avg = W/ t Instantaneous power P = dw/dt = (Fcosφ d)/dt = F v cosφ= F v Unit: watt 1 watt = 1 W = 1 J / s 1 horsepower = 1 hp = 550 t lb/s = 746 W kilowatt-hour is a unit or energy or work: 1 kw h = 3.6 M J