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PHYSICS UNIT 4: ENERGY & MOMENTUM

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WORK & KINETIC ENERGY Work, W: using a force, F, to displace an object a distance, d unit: Joule (1 J = 1 Nm) W = Fd W < Fd W = 0

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WORK & KINETIC ENERGY Work done by any force: W = Fd can be positive, negative, or zero Ex: sled sliding down a hill gravity does positive work friction does negative work normal force does no work d

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WORK & KINETIC ENERGY Power, P: the time rate at which work is done P = W/t unit: 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?

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WORK & KINETIC ENERGY Kinetic Energy, K: energy of motion energy: the ability to do work K = ½mv 2 unit: Joule scalar quantity – amount only – direction doesn’t matter If velocity doubles what happens to K?

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WORK & KINETIC ENERGY

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Work – Kinetic Energy Theorem: Work done on an object is equal to the total change in kinetic energy of the object W net = K f – K i F net d = ½mv f 2 – ½mv i 2

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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

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POTENTIAL ENERGY & CONSERVATION Potential Energy, PE: stored energy gravitational: energy of position due to gravity force Grav. PE = mgh h: height - measured from origin (reference point) unit: Joule, J can be positive, zero, or negative depending on choice of origin

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POTENTIAL ENERGY & CONSERVATION Potential Energy, PE spring : energy of position elastic: energy of position due to elastic force PE spring = ½kx 2 k: spring constant, x: stretch/compress distance unit: Joule can only be positive or zero

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Energy 101

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POTENTIAL ENERGY & CONSERVATION Conservation of Mechanical Energy: a system's total mechanical energy (K+U) stays constant if there is no friction K i + U i = K f + U f if there is friction, some K will be turned into other energy forms - heat, sound, etc. mechanical energy is not conserved total energy is still conserved

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PHYSICS UNIT 4: ENERGY & MOMENTUM

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MOMENTUM & IMPULSE Impulse, J: change in momentum produced by a force J = change in P, = Ft unit: kg m/s

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MOMENTUM & IMPULSE Bouncing vs. Sticking in an impact ex: a 1000 kg car going +10 m/s hits a wall J = p f -p i sticking: p i = +10,000 kgm/s, p f = 0 J = –10,000 kgm/s bouncing: p i = +10,000 kgm/s, p f = – 10,000 kgm/s J = –20,000 kgm/s bouncing off at impact has up to twice the force of sticking

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MOMENTUM & IMPULSE angular momentum, L: amount of “rotation” an object has L = I : angular velocity, rad/s I : rotational inertia, resistance to rotation (due to mass and its distribution - same mass further from center has more I ), kgm 2 unit: kgm 2 /s

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MOMENTUM & IMPULSE Law of Conservation of Momentum: total momentum of a system of objects is constant if no outside forces act m i v i = m f v f if mass increases, velocity decreases (and vice versa)

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MOMENTUM & IMPULSE Law Conservation of Angular Momentum: total angular momentum of a system of objects is constant if no outside torques act I i i = I f f

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MOMENTUM & IMPULSE if rotational inertia increases, angular velocity decrease s (and vice versa)

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PHYSICS UNIT 4: ENERGY & MOMENTUM

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QUIZ 4.4 A 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/s -120,000 N -60,000 kgm/s 0 kgm/s

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PHYSICS UNIT 4: ENERGY & MOMENTUM

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COLLISIONS inelastic collision: objects collide and stick (or collide and deform) momentum is conserved, kinetic energy is not m 1 v 1 + m 2 v 2 = Mv 3 (M = m 1 + m 2 ) be sure to include + or – for velocity’s direction

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COLLISIONS Ex: 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?

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COLLISIONS propulsion or explosion: total initial momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero 0 = m 1 v 3 + m 2 v 4 or m 1 v 3 = –m 2 v 4 ex: rocket propulsion, gun recoil

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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?

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COLLISIONS elastic collision: objects collide and bounce off with no loss of energy both momentum and kinetic energy are conserved m 1 v 1 + m 2 v 2 = m 1 v 3 + m 2 v 4 ½m 1 v 1 2 + ½m 2 v 2 2 = ½m 1 v 3 2 + ½m 2 v 4 2

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QUIZ 4.4 A 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?

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PHYSICS UNIT 4: ENERGY & MOMENTUM

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UNIT 4 REVIEW K i + U i = K f + U f U g = mgh U e = ½kx 2 K = ½mv 2 W = Fdcos W net = K f – K i P = W/t 1.00 hp = 746 W p = mv J = p f – p i = Ft L = I I i i = I f f m 1 v 3 = –m 2 v 4 m 1 v 1 + m 2 v 2 = Mv 3 m 1 v 1 + m 2 v 2 = m 1 v 3 + m 2 v 4

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