# PHYSICS UNIT 4: ENERGY & MOMENTUM

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PHYSICS UNIT 4: ENERGY & MOMENTUM

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 = 0 W < Fd

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

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?

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 If velocity doubles what happens to K?

WORK & KINETIC ENERGY

WORK & KINETIC ENERGY Work – Kinetic Energy Theorem: Work done on an object is equal to the total change in kinetic energy of the object Wnet = Kf – Ki Fnetd = ½mvf2 – ½mvi2

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

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

POTENTIAL ENERGY & CONSERVATION
Potential Energy, PEspring: energy of position elastic: energy of position due to elastic force PEspring = ½kx2 k: spring constant, x: stretch/compress distance unit: Joule can only be positive or zero

Energy 101

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 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

UNIT 4: ENERGY & MOMENTUM
PHYSICS UNIT 4: ENERGY & MOMENTUM

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

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 angular momentum, L: amount of “rotation” an object has L = Iw w: angular velocity, rad/s I: rotational inertia, resistance to rotation (due to mass and its distribution - same mass further from center has more I), kgm2 unit: kgm2/s

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)

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

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

UNIT 4: ENERGY & MOMENTUM
PHYSICS UNIT 4: ENERGY & MOMENTUM

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 0 kgm/s -60,000 kgm/s -120,000 N

UNIT 4: ENERGY & MOMENTUM
PHYSICS UNIT 4: ENERGY & MOMENTUM

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

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?

COLLISIONS propulsion or explosion: total initial momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero 0 = m1v3 + m2v4 or m1v3 = –m2v4 ex: rocket propulsion, gun recoil

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?

COLLISIONS elastic collision: objects collide and bounce off with no loss of energy both momentum and kinetic energy are conserved m1v1 + m2v2 = m1v3 + m2v4 ½m1v12 + ½m2v22 = ½m1v32 + ½m2v42

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?

UNIT 4: ENERGY & MOMENTUM
PHYSICS UNIT 4: ENERGY & MOMENTUM

UNIT 4 REVIEW Ki + Ui = Kf + Uf Ug = mgh Ue = ½kx2 K = ½mv2 W = Fdcosq
Wnet = Kf – Ki P = W/t 1.00 hp = 746 W p = mv J = pf – pi = Ft L = Iw Iiwi = Ifwf m1v3 = –m2v4 m1v1 + m2v2 = Mv3 m1v1 + m2v2 = m1v3 + m2v4