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Virginia Tech - Study Guide - Final

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Ch 7 - Momentum

Ch 6 - Work & Energy

Work = Joules

and Shartaut - Linear Womentum Corsarvation Theorem NII: IF = (Ap/t)

useful for collisions p = mv (p = momentum)

** on a system of particles is 0,

then Pis conserved constant) pis a vector in (kg*m/s)

P - SP = = al particles Ap = impulse

2 Types of Colisions = p = p is true for both 1. Indlastic (most general) KEKE, 2 Elasia (special case) KE = KE

NII: SF = (Ap / A:)

IF O, then P

P

O

Y

Elastic Collision Choose ayatom (my, m} Dm

in terms of m., m. V. Start p = p. m, V. + 0 = m. V.. + m.V. KE = KE

IF is constant: W = F AX

Hooke's Law - Plat F vsx

. W = area under curve Hooke's Law F = kx

k> is constant

• W. - ("%) kx Summary:

W = F || Arcos[e) F = kx

W. - -(kx 1st Shortcut-WKE

KE = (mv (Joules)

*No conditions, applies all the time

• W - AKE = mv.' -.my

#Nat the most practical to use KE,+ PE = KE,+ PE, Vimy + mgh - Kmv. + mgh,

• Total energy: E = KE + PE 2nd Shortcut. Special Case of WKEEcarservation E - E Fall forces that do work on a particle are conservative, then Eis conscrved (constant) 1 Graph

2 Graph W.. = mgår los(180) W = (k

VTI

Ballistic Penculum 1 = 2: inclastic collision P = P = P.-P. 2 3: simple pendulum

KE,+ PE = KE,+ PE, V + HATV,+ m igh; NV + (m. Watu

H..(1/29 (V)

H... = (1/2g1[mV./ (M + my Explosions: Collisions in Reverse

my,+OM+mW

3 Graph W = F. W. = -1.mga

Aroos(180)

So, 0 = m. V.,+ m, V So.V = (

m m )(V...

Summary:

In all 3 cases, some force did negative work w mg and F., we can get back any work we did against them

w'F., our work against it disappears Poterial Encroy APE - W

Foroes that have PE are called conservative (mg. F.) PE=mgy Forces wo PE (F) are called non conservative PE = ax If you want to learn more check out certified veterinary assistant study guide

**Not true in case 3

Ch 5 - Uniform Circular Motion (Special NII)

Ch 8 - Rotational Kinematics

UCM is a rotation V. 10 motion

.bonita

W

Frequency (f) - # of cycles / time = Hz Period (T) -time required for one cycle = seo On a circular path: a = vir

a's point to center Force:

What provides 2 SF = my Ir

Tangential and radial direction Other forcers (mg. T, N, FJ must provide

E = TE NEVER put on a FDD General Method for UCM problems

Identify UCM There must be a contripcial force (F ) What provides Fox?

o mg.T, NF. Fan = IFirdai

0 Ignore all non-radial forces 5. For = mvir

Solve for unknown

forCCW) rotations <0 for clockwise (CW) rotations S-OS-ROS - RO - SIR C = 2m 1 rad - 360° / 2

19 - 20 / 360°

-oc

w] = [e]/[:] = rad / s = 1/ses" (a= [] / [L] = radis / s = rad Ist1/= 54

Studs

1+ Yout

What kind of motion?" Constant w (a = 0) Constant ( 0) Variable a difficult) We also discuss several other topics like raymond sadeghi utsa

e(t) =

(t) = 4

. + +

(t) = 44, + ai

Drawina Below: Sl: = re/ -- VIE= mit

Alta hah

V =

w

Ch 4.7 - Newtonian Gravity The planets move in (approximatcly circular orbits abt the sun

Plarats execute UCM - Must have a centripetall force We also discuss several other topics like the most dramatic type of resocialization is

We also discuss several other topics like syracuse university advertising

We also discuss several other topics like ant 105

What provides it? Gravitational force-name given

to For G = 8.67 x 109 Nm/kg

. For small m's, E l is small Near sfc F = GM-m RM

. G(M! (R) - 9.8m's

Rolling wla Sicping V = Rw KE - KV+ XIV

Moment of Inertia of object abt axis:

1 = Smr Rotacional equivalent to m KE- [mr]

RH

S.=re

FEGIM

Helpful Formulas:

S = req =2 = rw' (radial component) V = a = ra (tangential component)

Ch 9 - Rotations of Rigid Extended Obj Abt Fixed Axis

Enter what else you need here!

10 L

To computer of any Fabt any point P: 1. rlocates point of application of Fw.r.t. 2. Pratond r extends angle bhw imagined extension of r and F 3. ==rF sin(a)

0 Li

-On

.

IF | = | F | sin(o)

> O if Ftends to cause a CCW rotation abi axis

0 Not really important . O if F tends to cause a CW rotation abt axis . SI: 1] = N m - J

Center of Mass Nil in Tangentia Direction

Y "X=1/M Imx

• IF. = mra . F sino) = mro

. | F | sini) - mrat General Motion Inertis

E = KE+KE,+ PE = YNV + Xw+ PE (NII, Sc = la

Rolling w'a slipping: V = rw T= ma looks like F = ma 1 = mr

Angular Homerum: L = w # Moment of incrtia of m ab: axis

L O for CCW rotations * Rotational analogue to m

LCO for CW rotations ++.Given a uniform extended object L-u r ip sino) ww/ sufficient symmetry, Mg acts on center L.corsarvation: * = 0, then L = L (rotational collisions)

Ch 11 - Fluids

Ch 17 - Sound

Pressure due to a column of fluid P[h) - pgh (+ P.)

Definitions Density (ko'm) p = m/V Pressure (Pa-Pascal)

P- FIA

= 1.01x10 Pa

Pascals Principle If you want to learn more check out chemistry 20a ucla

P = FTIA P = pgh+P

Intensity of a Sound Wave (W/m) Intensity U =

Speed of sound in air. - 343 m's

< 20 Hz subsound's > 20,000 Hz wrasounds 20 Hzstus 20.000 Hz

Doncler Effect

Hydraulic Lift | F,I AIAFI

V

.

Decibel Scale Definition: D = 10logo/

baseline intensity = 10-Wm intensity is inversely proportional to the square of the distance Ul. = (d.dy

Archimedes' Principle

F. l = weight of displaced fluid IF I - POV V = volume of displaced fluid (it) PV = mass of t. pVg = weight of it For incompressible from licuida!

p

Fluids in Motion m = P.V. - p.A.W.A m; = P. Avt m = m; = P.A.V. = PAV.

Bemulli's Ecuation

ov + pgh = const P: + 2, Y + P gh. = P. + Key + Pogh,

Ch 10 - Simple Harmonic Motion

Ch 16 - Waves

V= - - V - Af True for any periodic wave

10 Wave on a String - Transverse (1) 1. Physical displacement from equilibrium configuration 2. Since Vis constant, V =

VES .F=Fy in ms 3. Medium required: string

Most waves require a mecium (mechanical waves). some don't Some waves do not w=26/T: VA

AL = 12.312.5X2.... const interference desi AL = 0.12.21... const remains const

*special case of an oscillation abdan oquilibrium point "special case of periodic mation Period (T): time (sec) required for one cycle Frequency (f) number of cycles per second (Hz)

Period for a Penculum P=/T

T =

27 g

g=9.m/s Definition: a paride executes SHM

I = length of pendulum in meters ab: equilibrium SF = kx

- k> constar

• I deviation from equilibrium

. Case of variable acceleration For any particle in 1D SHM (let w = 21 IT)

= A (amplitude) x{t) = A295/2013/T) OR X[t] = roost) Y = Aw # 1 s sin cos $ 1"

(t) = 2/Tsin(2t/T) OR ft) = -rousin(t) a(t) = N2m/T)*os(2T/T) OR a(t) = -w'oost) Period of a block Spring System Can we use anergy conservation for SHM?

u = 2/T= v =T-2 VME SF = kx is it conservative? E conservation valid for SHM T = 20 / w w- 2mf = 2mT It is PE = kx

mv + Ykx = constant

Observed Sinbla Patterns Nust fit n(N2) = L .- 2Ln f-LEHmL)) (n)

2L

Periodic Waves lancial casel Wavelength (A): length (m) of one cycle

Amplitude (A): maximum

value of disturbance

References: