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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 hillgravity does positive workfriction does negative worknormal 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 = ½mv2 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 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 – ½mvi
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, 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
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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 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
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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 = 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 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), kgm2
unit: kgm2/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 mivi = mfvf 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 Iii= Iff
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MOMENTUM & IMPULSE
if rotational inertia increases, angular velocity decreases (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/s0 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
m1v1 + m2v2 = Mv3 (M = m1 + m2)
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 = m1v3 + m2v4 or m1v3 = –m2v4
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
santa elastic.IP
both momentum and kinetic energy are conserved
m1v1 + m2v2 = m1v3 + m2v4
½m1v12 + ½m2v2
2 = ½m1v32 +
½m2v42
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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 Ki + Ui = Kf + Uf
Ug = mgh Ue = ½kx2
K = ½mv2
W = Fdcos Wnet = Kf – Ki
P = W/t 1.00 hp = 746 W
p = mv J = pf – pi = Ft
L = I Iii = Iff
m1v3 = –m2v4
m1v1 + m2v2 = Mv3
m1v1 + m2v2 = m1v3 + m2v4