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