work, energy & momentum. work & kinetic energy work, w: using a force, f, to displace an...
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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 (1 J = 1 Nm)
W = Fd W = (Fcos)d W = 0
WORK & KINETIC ENERGY Work done by any force: W = Fdcos
can be positive, negative, or zero
Ex: sled sliding down a hillgravity does positive workfriction does negative worknormal force does no work
d
d
F
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
Weight
Thrust
Drag
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
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
Fnetdcos = ½mvf2 – ½mvi
2
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 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
POTENTIAL ENERGY & CONSERVATION
pendulum:
U K
K U
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
Example: a Mass in Free Fall
Ki + Ui = Kf + Uf
½mvi2 +
mghi = ½mvf
2 + mghf
Cons. Of Energy
POTENTIAL ENERGY & CONSERVATION
Example: a Mass on a Horizontal Spring
½mvi2 + ½kxi
2 = ½mvf2 + ½kxf
2 Ki + Ui = Kf + Uf
POTENTIAL ENERGY & CONSERVATION
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 throughout its flight.
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 his energy go?
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 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
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 N s
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)
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
-120,000 N
-60,000 kg m/s
0 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 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 m1v1 + m2v2 = Mvf (M = m1 +
m2) 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 m1v1o + m2v2o = m1v1f + m2v2f
½m1v1o2 + ½m2v2o
2 = ½m1v1f2 +
½m2v2f2
Useful Equations p = mv J = pf – pi = Ft
m1v3 = –m2v4
m1v1 + m2v2 = Mv3
m1v1 + m2v2 = m1v3 + m2v4