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WORK, ENERGY & MOMENTUM WORK & KINETIC ENERGY Work, W: using a force, F, to displace an object a distance, d unit: Joule W = Fd (1 J = 1 Nm) W = (Fcosq)d W=0 WORK & KINETIC ENERGY d Work done by any force: W = Fdcosq can be positive, negative, or zero q F Ex: sled sliding down a hill gravity does positive work friction does negative work normal force does no work d WORK & KINETIC ENERGY Power, P: the time rate at which work is done Lift Thrust Drag P = W/t unit: Watt, W (1 W = 1 J/s) (1 J/s = 1 Nm/s) Weight english unit: horsepower, hp (1.00 hp = 746 W) P = Fv WORK & KINETIC ENERGY Kinetic Energy, K: energy of motion Energy: the ability to do work 2 K = ½mv unit: Joule scalar quantity – amount only – direction doesn’t matter can only be zero or positive – never negative WORK & KINETIC ENERGY WORK & KINETIC ENERGY Work/Energy Theorem: net work done on an object is equal to the total change in kinetic energy of the object Wnet = Kf – Ki 2 2 Fnetdcosq = ½mvf – ½mvi WORK & KINETIC ENERGY Net work determines the change in an object’s motion positive work = increase in kinetic energy (speed up) Ex: throwing a ball negative work = decrease in kinetic energy (slow down) Ex: catching a ball zero work = no change in kinetic energy Ex: weightlifting PHYSICS UNIT 4: ENERGY & MOMENTUM POTENTIAL ENERGY & CONSERVATION Potential Energy, U: energy of position Gravitational PE: energy of position due to gravity force PE = mgh g h: height, measured from origin (reference point) unit: Joule, J Scalar Quantity - can be positive, zero, or negative depending on choice of origin POTENTIAL ENERGY & CONSERVATION pendulum: UK KU the amount stays the same POTENTIAL ENERGY & CONSERVATION Conservation of Mechanical Energy: a system's total mechanical energy (K+U) stays constant if there is no friction Ki + Ui = Kf + Uf However, if there is friction, some K will be turned into other energy forms - heat, sound, etc. Ki + Ui = Kf + Uf + Wlost mechanical energy is not conserved total energy is still conserved Cons. Of Energy Example: a Mass thrown in the air. Ki + Ui = Kf + Uf 2 ½mvi + mghi = ½mvf2 + mghf POTENTIAL ENERGY & CONSERVATION Example: a Mass on a Horizontal Spring Ki + Ui = Kf + Uf 2 2 2 2 ½mvi + ½kxi = ½mvf + ½kxf PHYSICS UNIT 4: ENERGY & MOMENTUM QUIZ 4.1 Joe throws a ball straight up into the air, and catches it on the way back down. (a) Draw a graph showing the kinetic energy of the ball throughout its flight. (b) Draw a graph showing the gravitational potential energy of the ball throughout its flight. (c) Draw a graph showing the total energy of the ball PHYSICS UNIT 4: ENERGY & MOMENTUM QUIZ 4.2 (a) Tell what kinds of energy a pole vaulter has at each of the four points labeled on the picture above (point 4 is just before hitting the mat) (b) After the pole vaulter hits the mat, his total energy is zero. Where did all PHYSICS UNIT 4: ENERGY & MOMENTUM QUIZ 4.3 A roller coaster car, mass 500 kg, starts from rest at the top of a hill 30 m above 147,000 J ground level. Ignore friction. (a) What 147,000 energy J is the car’s potential at the top m/s car’s kinetic of the hill? (b) What 24.2 is the energy at the bottom of the98,000 hill?J (c) How fast will the car be going at the bottom of the hill? (d) What is the car’s PHYSICS MOMENTUM MOMENTUM & IMPULSE Momentum, p: amount of “umph" an object has (Inertia in Motion) = mv unit p : kg m/s vector quantity - includes direction +2 kgm/s –2 kgm/s MOMENTUM & IMPULSE Impulse, J: A force that acts over a duration of time. J = Ft unit: kg m/s or Ns MOMENTUM & IMPULSE Impulses cause a change in momentum. This is known as the Impulse-Momentum Theorem. It is analogous to the Work-Energy Theorem. FΔT = Δp = pf – pi = mvf -mvi unit: kg m/s or N s force of impact, F = -pi/t to decrease force of impact, decrease p (decrease v i before impact) or increase t (catching an egg; stunt falling; air bags) Practice A 2000 kg car going 30 m/s hits a brick wall and comes to rest. (a) What is the car’s initial momentum? 60,000 kg m/s (b) What is the car’s final 0 kg m/s momentum? (c) What impulse does the wall give -60,000 kg m/s to the car? (d) If the impact takes 0.5 seconds, -120,000 N what force is exerted on the car? MOMENTUM & IMPULSE Bouncing vs. Sticking in an impact ex: a 1000 kg car going +10 m/s hits a wall J = pf-pi sticking: pi = +10,000 kgm/s, pf = 0 J = –10,000 kgm/s bouncing: pi = +10,000 kgm/s, pf = – 10,000 kgm/s J = –20,000 kgm/s bouncing off at impact has up to twice the force of sticking MOMENTUM & IMPULSE Law of Conservation of Momentum: total momentum of a system of objects is constant if no outside forces act mivi = mfvf if mass increases, velocity decreases (and vice versa) COLLISIONS inelastic collision: objects collide and stick (or collide and deform) momentum is conserved, kinetic energy is not BEFORE = AFTER m v + m v = Mv (M = m1 + m2) 1 1 2 2 f be sure to include + or – for velocity’s direction COLLISIONS propulsion or explosion: total initial momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero 0 = m1v1f + m2v2f or m1v1f = –m2v2f ex: rocket propulsion, gun recoil COLLISIONS Ex: A 4 kg rifle fires a 0.050 kg bullet, giving the bullet a final velocity of 300 m/s east. What is the recoil velocity of the rifle? COLLISIONS elastic collision: objects collide and bounce off with no loss of energy both momentum and kinetic energy are conserved BEFORE = AFTER m v 1 1o + m2v2o = m1v1f + m2v2f 2 + ½m v 2 = ½m v 2 + ½m v 2 ½m v 1 1o 2 2o 1 1f 2 2f Useful Equations p = mv J = pf – pi = Ft m1v3 = –m2v4 m1v1 + m2v2 = Mv3 m1v1 + m2v2 = m1v3 + m2v4