Mac Pro (Original)
Backside of a Power Mac G5 (left) and a Mac Pro (right). 2008
For external connectivity, the Mac Pro included five USB 2.0 and four FireWire 800 ports.
Page 1 of 2
Side view of a Power Mac G5 (left) and an Mac Pro (right), 2008
Retrieve
Work Done by an External Force
Previously we have looked at the work done to/from an object.
We can extend this to a system of more than one object.
Work is the energy transferred to or from a system by means of an
external force acting on that system.
No
The Potential Energy Curve
For the 1 - D case, the work done, W , by a force, F , moving an
object thr ough a displacement, x equals, Fx , therefore , the
potential energy can be written as
U x
dU x
U x W Fx F
x
dx
e.g ., Hooke' s Law, if the elastic p
Equilibrium Points
Equilibrium Points: refer to points where, dU/dx=-F(x)=0.
Neutral Equilibrium: is when a particles total mechanical energy is
equal to its potential energy (i.e., kinetic energy equals zero). If no
force acts on the particle, then dU/dx
Determining
Potential
Energy
Values
x
x
W F ( x)dx , U F ( x)dx . For GRAVIT. POT. ENERGY,
f
f
xi
xi
yf
yf
yi
yi
yf
U F ( y )dy mg dy mg dy mg y f yi
yi
U grav mg y f yi mgy
Only CHANGES in gravitatio nal Pot. energy are meaningful,
i.e., it is usual to d
8: Potential Energy & Conservation of Energy
POTENTIAL ENERGY (U) is the energy which can be associated with
configuration of a systems of objects. i.e. The position of an object
Also defined as the energy due to the position of the object
One example is
Conservation of Mechanical Energy
The mechanical energy is the sum of kinetic and potential energies,
Emech K U . If the system is isolated from its environmen t and
no external force causes any internal energy changes,
K W & U W , K U K f K i U f U i
K
Example 2:
A man of mass, m, jumps from a
ledge of height, h above the ground,
attached by a bungee cord of length
L. Assuming that the cord obeys
Hookes law and has a spring constant,
k, what is the general solution for the
maximum extension, x, of the c
Conservation of Energy
This states that
The total energy of a system, E, can only change by amounts of
energy that are transferred to or from the system.
Work done can be considered as energy transfer, so we can write,
W E Emec Eth Ein
Emec is the chang
Turning Points
For conservative forces, the
mechanical energy of the system
is conserved and given by,
U(x) + K(x) = Emec
where U(x) is the potential energy
and K(x) is the kinetic energy.
K 0 at ymax , Emec mgymax
F ( y )
Emec K ( y ) U ( y )
Therefore,
Example 1:
A child of mass m slides down a helter
skelter of height, h. Assuming the
slide is frictionless, what is the speed of
the child at the bottom of the slide ?
h=10m
From the CONSERVATI ON OF MECHANICAL ENERGY,
Emec ,i Emec , f U i K i U f K f
1 2
Nkz do we head GQULunHwn Mcchkvcs 7
A)- Hqc. and 4) he my Cerurx Ii; several
ra HMA we. how cal Classic
PM 3'45 Scam I? be. in exceHeN Shave.
Meckowas haul Oxovamcca m Hat Hm:
Newbh *9 ECCOMC Ox PYQA\-C_HVC h), EYCCCSQ
ow \A )O OUA unknown \0\ NC DVM-c
'
QMSL t Oh -c('\W\CV\simu| Y0b\&
Consfoer 0\ box 4] S\2e_ a W.IHA \mbh Wang,
_
7: D V0) _
2M 0 -g<x<0 9
mm '
Th; Fanaw/o Pach\c in (A box (107:1stle
Lb Hm. ,Qimu Voeao
Ami-m \IW enev o 4 < Va
:D LS easicsL R \vc Ha: BYO\o\cw\ in Hag
Xb ang wiLk wave vx
Somc Ncce ssovz MONA
Tau win [town HAKI W05? oocroJ'DYS 3n QM
w are OmHQihear So kaywc
abomL Qmtnv .9 aces.
0w ' a
ee. In? Tex/Kev) $
A ,Qvxehr .gEace (0f 1:ch shame) ii OVCY a
oL'cob
NOVA cfw_s
Como\tx numbers has
3 k W S
'ieJo F read cr
how 0\9 Vcchyrs
Tho; C45 I a fin? 0(th I eisehberig
Uncerlgnnlg rgijamg
AMJ-Wh
HI" ? \l(i1 l
W
wk'mk has \0 SAHSEZ Ha: SckYBG'Unm' Egg
Thus
Now
_-
L133 Wm) - HWtD 3
3 = -il\1lu;)> and 9< H: M (my-n
f
consider Has Hmcde ehdchcc
owe o erHV 0 made 2 L a mlH-s
o
x \idr
The H m3 Wan am,
imc - dcvdo oMehF om Wk 14)
ankle). W>= Hulk) 9
H is We. Hon/minbniom 0x Mcrmihnn o crakw'.
WWW
b
Sml- \an Hm: La ram Com ormvs\oJlo\n
96$;le WCCMNA'Ics ceaivx wKEM ehera\'\Z-4I
COOYc\n0\-es . and Hngw- emeralie dodHCS
O 3 akc 0x Le chok
Midterm Due Monday Oct 5, 11am
September 25, 2015
Do not talk or communicate in any other way with anyone other than
me about this midterm. Any such communication is a breach of academic
integrity, and will be considered sufficient grounds for a failing g
Physics 232: Worksheet 2
September 1, 2016
Please show all the intermediate steps for your benefit.
1. Probelm 1
A small plastic ball with mass m is suspended by a string with length L in a
uniform electric field E as shown in Figure. The ball is in equil
PHY 242
Lab 2: Function Generator and Oscilloscope.
Introduction
Last lab we introduced the ideas of Voltage, Current, and Resistance. This week we will explore
these ideas again, however these quantities will be changing in time. One way to make things
c
Physics 232 : Formula sheet for Midterm 1
1. Coulombs law :
q1 q2
~ 12 ,
F~12 = ke 2 r12 = q2 E
r12
where F~ , ke , q1 , q2 , ~r12 are the force, ke =
2
with the 0 = 8.85 1012 NCm2 as the permittivity of
~ 12 is the electric field sue
the free space, char
Physics 232
Electricity, Magnetism & Physical Optics
Class Schedule (subject to change)
Month
Aug
Aug
Aug
Aug
Aug
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
Oct
N
Physics 232: Solutions for Worksheet 4
September 15, 2016
Please show all the intermediate steps for your benefit.
1. Problem 1
Find the potential at point X, a distance R from a point charge +Q.
Sol: The potential is V = ke Q
R.
2. Problem 2
Distribute t
Physics 232: Vector Calculus Review
August 25, 2016
Please show all the intermediate steps for your benefit.
Tom and Jane are both trying to get to the soda machine on the 2nd floor from the
doorway of a room on the 1st floor. They decide to take differen
Physics 232: Worksheet 4
September 15, 2016
Please show all the intermediate steps for your benefit.
1. Problem 1
Find the potential at point X, a distance R from a point charge +Q.
2. Problem 2
Distribute the charge +Q uniformly over an arc length of rad
Physics
HS/Science
Unit: 03 Lesson: 01
Day 2 Kinematics Problems KEY
(Show all work)
1.
If a car starts from rest and accelerates at 5.0 m/sec 2 for 6.0 seconds, how far did it travel and
how fast was it moving at the end of the 6.0 seconds?
x = v0t + at2
Physics
HS/Science
Unit: 02 Lesson: 01
Using a Photogate to Measure g
Pasco DataStudio Software
Introduction:
An object in free fall near the Earths surface accelerates downward at a constant rate. This
acceleration is usually represented with the symbol