2 WORK & KINETIC ENERGYWork, W: using a force, F, to displace an object a distance, dunit: Joule (1 J = 1 Nm)W = FdW = 0W < Fd
3 WORK & KINETIC ENERGY Work done by any force: W = Fd can be positive, negative, or zerodEx: sled sliding down a hillgravity does positive workfriction does negative worknormal force does no work
4 WORK & KINETIC ENERGY Power, P: the time rate at which work is done P = W/tunit: Watt, W (1 W = 1 J/s = 1 Nm/s)english unit: horsepower, hp (1.00 hp = 746 W)What happens to power with twice work?What happens to power with ½ the time?
5 WORK & KINETIC ENERGY Kinetic Energy, K: energy of motion energy: the ability to do workK = ½mv2unit: Joulescalar quantity – amount only – direction doesn’t matterIf velocity doubles what happens to K?
7 WORK & KINETIC ENERGYWork – Kinetic Energy Theorem: Work done on an object is equal to the total change in kinetic energy of the objectWnet = Kf – KiFnetd = ½mvf2 – ½mvi2
8 WORK & KINETIC ENERGYnet work determines the change in an object’s motionpositive work = increase in kinetic energy (speed up)Ex: throwing a ballnegative work = decrease in kinetic energy (slow down)Ex: catching a ballzero work = no change in kinetic energyEx: weightlifting
9 POTENTIAL ENERGY & CONSERVATION Potential Energy, PE: stored energygravitational: energy of position due to gravity forceGrav. PE = mghh: height - measured from origin (reference point)unit: Joule, Jcan be positive, zero, or negative depending on choice of origin
10 POTENTIAL ENERGY & CONSERVATION Potential Energy, PEspring: energy of positionelastic: energy of position due to elastic forcePEspring = ½kx2k: spring constant, x: stretch/compress distanceunit: Joulecan only be positive or zero
12 POTENTIAL ENERGY & CONSERVATION Conservation of Mechanical Energy: a system's total mechanical energy (K+U) stays constant if there is no frictionKi + Ui = Kf + Ufif there is friction, some K will be turned into other energy forms - heat, sound, etc.mechanical energy is not conservedtotal energy is still conserved
13 UNIT 4: ENERGY & MOMENTUM PHYSICSUNIT 4: ENERGY & MOMENTUM
14 MOMENTUM & IMPULSE Impulse, J: change in momentum produced by a force J = change in P, = Ftunit: kg m/s
15 MOMENTUM & IMPULSE Bouncing vs. Sticking in an impact ex: a 1000 kg car going +10 m/s hits a wallJ = pf-pisticking: pi = +10,000 kgm/s, pf = 0J = –10,000 kgm/sbouncing: pi = +10,000 kgm/s, pf = – 10,000 kgm/sJ = –20,000 kgm/sbouncing off at impact has up to twice the force of sticking
16 MOMENTUM & IMPULSEangular momentum, L: amount of “rotation” an object hasL = Iww: angular velocity, rad/sI: rotational inertia, resistance to rotation (due to mass and its distribution - same mass further from center has more I), kgm2unit: kgm2/s
17 MOMENTUM & IMPULSELaw of Conservation of Momentum: total momentum of a system of objects is constant if no outside forces actmivi = mfvfif mass increases, velocity decreases (and vice versa)
18 MOMENTUM & IMPULSELaw Conservation of Angular Momentum: total angular momentum of a system of objects is constant if no outside torques actIiwi = Ifwf
20 UNIT 4: ENERGY & MOMENTUM PHYSICSUNIT 4: ENERGY & MOMENTUM
21 QUIZ 4.4A 2000 kg car going 30 m/s hits a brick wall and comes to rest. (a) What is the car’s initial momentum? (b) What is the car’s final momentum? (c) What impulse does the wall give to the car? (d) If the impact takes 0.5 seconds, what force is exerted on the car?60,000 kgm/s0 kgm/s-60,000 kgm/s-120,000 N
22 UNIT 4: ENERGY & MOMENTUM PHYSICSUNIT 4: ENERGY & MOMENTUM
23 COLLISIONSinelastic collision: objects collide and stick (or collide and deform)momentum is conserved, kinetic energy is notm1v1 + m2v2 = Mv (M = m1 + m2)be sure to include + or – for velocity’s direction
24 COLLISIONSEx: An 8000 kg truck going 10 m/s N collides with a 1000 kg car going 5 m/s S and their bumpers lock. How fast are the truck & car going after the collision?
25 COLLISIONSpropulsion or explosion: total initial momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero0 = m1v3 + m2v4 or m1v3 = –m2v4ex: rocket propulsion, gun recoil
26 COLLISIONSEx: A 4 kg rifle fires a kg bullet, giving the bullet a final velocity of 300 m/s east. What is the recoil velocity of the rifle?
27 COLLISIONSelastic collision: objects collide and bounce off with no loss of energyboth momentum and kinetic energy are conservedm1v1 + m2v2 = m1v3 + m2v4½m1v12 + ½m2v22 = ½m1v32 + ½m2v42
28 QUIZ 4.4A 1 kg soccer ball going 8 m/s hits a player’s 4 kg head (which is not moving before the hit). The soccer ball bounces back in the opposite direction (-) at 8 m/s. There is no loss of energy. (a) What kind of collision is this? (b) What conservation of momentum equation applies? (c) What is the velocity of the player’s head after the collision?
29 UNIT 4: ENERGY & MOMENTUM PHYSICSUNIT 4: ENERGY & MOMENTUM
30 UNIT 4 REVIEW Ki + Ui = Kf + Uf Ug = mgh Ue = ½kx2 K = ½mv2 W = Fdcosq Wnet = Kf – KiP = W/t1.00 hp = 746 Wp = mvJ = pf – pi = FtL = Iw Iiwi = Ifwfm1v3 = –m2v4m1v1 + m2v2 = Mv3m1v1 + m2v2 = m1v3 + m2v4