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WORK, 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 = (Fcosq)d W = 0

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**WORK & KINETIC ENERGY Work done by any force: W = Fdcosq**

can be positive, negative, or zero d Ex: sled sliding down a hill gravity does positive work friction does negative work normal force does no work

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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 J/s = 1 Nm/s) english unit: horsepower, hp (1.00 hp = 746 W) P = Fv Lift Thrust Drag Weight

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**WORK & KINETIC ENERGY Kinetic Energy, K: energy of motion**

Energy: the ability to do work K = ½mv2 unit: Joule scalar quantity – amount only – direction doesn’t matter can only be zero or positive – never negative

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WORK & KINETIC ENERGY

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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 Fnetdcosq = ½mvf2 – ½mvi2

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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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**UNIT 4: ENERGY & MOMENTUM**

PHYSICS UNIT 4: ENERGY & MOMENTUM

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**POTENTIAL ENERGY & CONSERVATION**

Potential Energy, U: energy of position Gravitational PE: energy of position due to gravity force Ug = mgh h: height, measured from origin (reference point) unit: Joule, J Scalar Quantity - can be positive, zero, or negative depending on choice of origin

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**POTENTIAL ENERGY & CONSERVATION**

pendulum: U K K U the amount stays the same

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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 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

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**Cons. Of Energy Example: a Mass in Free Fall Ki + Ui = Kf + Uf**

½mvi2 + mghi = ½mvf2 + mghf

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**POTENTIAL ENERGY & CONSERVATION**

Example: a Mass on a Horizontal Spring Ki + Ui = Kf + Uf ½mvi2 + ½kxi2 = ½mvf2 + ½kxf2

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**POTENTIAL ENERGY & CONSERVATION**

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**UNIT 4: ENERGY & MOMENTUM**

PHYSICS UNIT 4: ENERGY & MOMENTUM

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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 throughout its flight.

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**UNIT 4: ENERGY & MOMENTUM**

PHYSICS UNIT 4: ENERGY & MOMENTUM

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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 his energy go?

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**UNIT 4: ENERGY & MOMENTUM**

PHYSICS UNIT 4: ENERGY & MOMENTUM

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QUIZ 4.3 A roller coaster car, mass 500 kg, starts from rest at the top of a hill 30 m above ground level. Ignore friction. (a) What is the car’s potential energy at the top of the hill? (b) What is the car’s kinetic energy at the bottom of the hill? (c) How fast will the car be going at the bottom of the hill? (d) What is the car’s kinetic energy at the top of the next hill, 10 m above ground level? 147,000 J 147,000 J 24.2 m/s 98,000 J

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PHYSICS MOMENTUM

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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

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MOMENTUM & IMPULSE Impulse, J: A force that acts over a duration of time. J = Ft unit: kg m/s or N s

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**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 pi (decrease v before impact) or increase t (catching an egg; stunt falling; air bags)

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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? (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 kg m/s 0 kg m/s -60,000 kg m/s -120,000 N

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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 = 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

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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 mivi = mfvf if mass increases, velocity decreases (and vice versa)

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COLLISIONS inelastic collision: objects collide and stick (or collide and deform) momentum is conserved, kinetic energy is not BEFORE = AFTER m1v1 + m2v2 = Mvf (M = m1 + m2) be sure to include + or – for velocity’s direction

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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 = m1v1f + m2v2f or m1v1f = –m2v2f ex: rocket propulsion, gun recoil

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COLLISIONS Ex: 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?

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COLLISIONS elastic collision: objects collide and bounce off with no loss of energy both momentum and kinetic energy are conserved BEFORE = AFTER m1v1o + m2v2o = m1v1f + m2v2f ½m1v1o2 + ½m2v2o2 = ½m1v1f2 + ½m2v2f2

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**Useful Equations p = mv J = pf – pi = Ft m1v3 = –m2v4**

m1v1 + m2v2 = Mv3 m1v1 + m2v2 = m1v3 + m2v4

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