Work & EnergyAP1 Ch7

Or, “Why don’t Taylor count HomeWORK as WORK?”

Knotes

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Nitty Gritty?Definitions?

WorkA force acting through a displacement

cosFdW

FdW

Work → a force acting through a displacement

cosFdW

F

Fcos

Figure 7.3(a) A graph of F cos θ vs. d , when F cos

θ is constant. The area under the curve represents the work done by the force.

(b) A graph of F cos θ vs. d in which the force varies. The work done for each interval is the area of each strip; thus, the total area under the curve equals the total work done.

Nitty Gritty?Definitions?

EnergyWorkPE mghPE

Why?

FdW

dmaW )(

gPEmghW

Nitty Gritty?Definitions?

EnergyKE 2

21 mvKE

Why?

FdW

madW

2

)(22if vv

mW

admW

2022

ifvmW

KEv

mW f

2

2

Figure 7.8

The speed of a roller coaster increases as gravity pulls it downhill and is greatest at its lowest point. Viewed in terms of energy, the roller-coaster-Earth system’s gravitational potential energy is converted to kinetic energy. If work done by friction is negligible, all ΔPEg is converted to KE .

PEi

KEBot

PE + KE

Figure 7.9

A marble rolls down a ruler, and its speed on the level surface is measured.

PETop

KEBot

Figure 7.10

(a) An undeformed spring has no PEs stored in it. (b) The force needed to stretch (or compress) the spring a distance x has a magnitude F = kx , and the work done to stretch (or compress) it

is (c) Because the force is conservative, this work is stored as potential energy (PEs) in the spring, and it can be fully recovered.(d) A graph of F vs. x has a slope of k , and the area under the graph is . Thus the work done or potential energy stored is

Figure 7.12

A toy car is pushed by a compressed spring and coasts up a slope. Assuming negligible friction, the potential energy in the spring is first completely converted to kinetic energy, and then to a combination of kinetic and gravitational potential energy as the car rises. The details of the path are unimportant because all forces are conservative—the car would have the same final speed if it took the alternate path shown.

Figure 7.15

Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system.(a) system with only conservative forces. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air

resistance) because the force in the spring is conservative. The spring can propel the rock back to its original height, where it once again has only potential energy due to gravity.

(b) A system with nonconservative forces. When the same rock is dropped onto the ground, it is stopped by nonconservative forces that dissipate its mechanical energy as thermal energy, sound, and surface distortion. The rock has lost mechanical energy.

Figure 7.16

A person pushes a crate up a ramp, doing work on the crate. Friction and gravitational force (not shown) also do work on the crate; both forces oppose the person’s push. As the crate is pushed up the ramp, it gains mechanical energy, implying that the work done by the person is greater than the work done by friction.

Figure 7.19

Rolling a marble down a ruler into a foam cup.

KEBot

PETop

Figure 7.19

Rolling a marble down a ruler into a foam cup.

MVTotal MVBall

Figure 7.33

Figure 7.35

A man pushes a crate up a ramp.

Figure 7.36

The boy does work on the system of the wagon and the child when he pulls them as shown.

Figure 7.37 A rescue sled and victim are lowered

down a steep slope.

Figure 7.40

The skier’s initial kinetic energy is partially used in coasting to the top of a rise.

Nitty Gritty?Definitions?

EnergyPE in Spring

2

21 kxPE

FdW

kxxFdW

dFF

W

dFW

if

21

21

2

Work & Energy-Pt 2

Or, “Why don’t Taylor count HomeWORK as WORK?”

M

PE = mgh

h

M

PE = mgh

h

M

PE = mgh

h

M

PE = mgh

h

PE + KE

M

PE = mgh

h

PE + KE

M

PE = mgh

h

PE + KE

M

PE = mgh

h

PE + KE

KE

M

PE = mgh

h

PE + KE

KE

M

PE = mgh

h

PE + KE

KE

M

hghv

mvmgh

KP

221 2

PE PE

KE

PE PE

KE

h

L

PE PE

KE

h

L

)cos1( Lh

vh

H

gHt

gdt

2

2

hHd

gghHd

gHghd

tvd

h

h

h

hh

2

4

22

dh

vh

H

gHt

gdt

2

2

hHd

gghHd

gHghd

tvd

h

h

h

hh

2

4

22

dh

021

21 22

BotTop

BotBotTopTop

BottomTop

mvmghmv

PKPK

EE

BATMAN!

Power!Or “What the heck does a

horsepower have to do with a horse”?

tWP EW

tEP

tEP

tPEP

tmghP

I thought this was PHYSICS, not

PhysEd!

D

h

sec

)()( 2 ms

mkg

tmghP

What’s this unit?

N m JP Ws s

Advanced Shtuff?

cosb

a

W F dl

2

0

,

12

b

ax

So

W Fdx

W kxdx kx

Advanced Shtuff?;

( )

ConverselydWF xdx

drrMMGdrFW

r

r

r

rg

2

1

2

1

221

Advanced Shtuff?

2

1

2211r

r

drr

MGMW

Advanced Shtuff?

Eg

GmMW PE

r

Advanced Shtuff?

dE dxP F Fvdt dt

MomentumCh8

Or, “How to make Newton’s Laws even more complicated without

even trying…”

Daryl L TaylorGreenwich HS, CT

©2004, 2006, 2007, 2009, 2012 (Just in case…)

Nitty Gritty?Definitions?

‘member FMA?

F ma

vF mt

Ft m vFt mv

F ma

ImpulseLatin impulsus, from past participle of impellere, to impelImpel: See impulse…

MomentumLatin mōmentum, movement

Nitty Gritty?Definitions?

P Conservation

' '1 1 2 2 1 1 2 2

i fP P

m v m v m v m v

Why?

1 2

1 1 2 2

1 1 2 2

1 1 2 2

F Fm a m a

m v m vt t

m v m v

NL3

POP QUIZ;

#1

2-D MomentumMomentum is a linear vector

1 2

1 1 2 20 0m v m v

2-D MomentumAngles?

m1v1i

2-D MomentumAngles?

m1v1i

m1v1f

m2v2f

2-D MomentumAngles?

m1v1i

m1v1f

m2v2f

POP QUIZ;

#2

2.5 m/s

Figure 8.6 An elastic one-dimensional two-

object collision. Momentum and internal kinetic energy are conserved.

Figure 8.8

An inelastic one-dimensional two-object collision. Momentum is conserved, but internal kinetic energy is not conserved.

(a) Two objects of equal mass initially head directly toward one another at the same speed.(b) The objects stick together (a perfectly inelastic collision), and so their final velocity is zero. The internal kinetic

energy of the system changes in any inelastic collision and is reduced to zero in this example.

Figure 8.10

An air track is nearly frictionless, so that momentum is conserved. Motion is one-dimensional. In this collision, examined in Example 8.6, the potential energy of a compressed spring is released during the collision and is converted to internal kinetic energy.

Figure 8.11

A two-dimensional collision with the coordinate system chosen so that m2 is initially at rest and v1 is parallel to the x -axis. This coordinate system is sometimes called the laboratory coordinate system, because many scattering experiments have a target that is stationary in the laboratory, while particles are scattered from it to determine the particles that make-up the target and how they are bound together. The particles may not be observed directly, but their initial and final velocities are.

Figure 8.12 A collision taking place in a dark

room is explored in Example 8.7. The incoming object m1 is scattered by an initially stationary object. Only the stationary object’s mass m2 is known. By measuring the angle and speed at which m1 emerges from the room, it is possible to calculate the magnitude and direction of the initially stationary object’s velocity after the collision.

Figure 8.16

A small object approaches a collision with a much more massive cube, after which its velocity has the direction 1. The angles at which the small object can be scattered are determined by the shape of the object it strikes and the impact parameter .

Types of Collisions;Elastic

AND KE are conserved

i f

i fKE KE

Types of Collisions;Inelastic

ONLY are conserved

i f

POP QUIZ;

#3

MV & cm

cmCenter of Mass

NOT to be confused with Center of Gravity (cg)

mmvvcm

MV & cm

cmExamples

MV & cm

CmExamples

MV & cm

cm

MV & cmCm – Hume Beans

Bending overSittingStandingWalkingOne-Leg Lift (Wall & Free-standing)Butt against wall – Touch toesChair pick-upBabies vs Adults

Head size – ¼ vs 1/8

MV & cm

Cm – Hume BeansWile E. Coyote Videom-stick and hatRolling UP HILL demo

mmvv

mmxx

cm

cm