phy 113 a general physics i 11 am-12:15 p m mwf olin 101 plan for lecture 6:

PHY 113 C Fall 2013 -- Lecture 6 19/12/2013

PHY 113 A General Physics I11 AM-12:15 PM MWF Olin 101

Plan for Lecture 6:

Chapters 5 & 6 – More applications of Newton’s laws

1. Friction and other dissipative forces

2. Forces in circular motion


Isaac Newton, English physicist and mathematician (1642—1727)

http://www.newton.ac.uk/newton.html

1. In the absence of a net force, an object remains at constant velocity or at rest.

2. In the presence of a net force F, the motion of an object of mass m is described by the form F=ma.

3. F12 =– F21.

http://www.newton.ac.uk/newton.html


Webassign question from assignment #5


Webassign question from assignment #5 – continued

)m. ˆ4.40+ ̂(1.60

at rest at initially is that kg 1.90 of particle aon act N, ) ˆ6.30 + ˆ(2.70 = and N ) ˆ4.45 + ˆ(2.80 = forces, Two

i

21

jir

jiFjiF

m

m

F1

F2 2

21

21

ttt

ttm

m

ii

i

net

net

avrr

avv

Fa

aFFF

Nˆ75.10ˆ50.5

Nˆ6.304.45ˆ2.702.80

N, ) ˆ6.30 + ̂(2.70 ) ˆ4.45 + ˆ(2.80 = 21

ji

ji

jijiFF


Webassign question from assignment #5 – continued

m

F1

F2

2

21

21

ttt

ttm

m

ii

i

net

net

avrr

avv

Fa

aFFF

sttt

s

/mˆ658.5ˆ895.20

/mˆ658.5ˆ895.2kg90.1

Nˆ75.10ˆ50.5

Nˆ75.10ˆ50.5=

2

21

jiv

jijia

jiFF


Webassign question from Assignment #4

T T

mg mg sin q

aa

amgmTamgmT

22

11

sin q


Newton’s second law aF mnet

applied

g

FnFTF

jF

:surface a tonormal forceSupport :rope masslessin tension todue Force

ˆ :surface sEarth'near Gravity

:known have weForces

n

mg

TaTF

:ssfrictionle is surface Ifmnet


mg

nT

Another example of motion along a frictionless surface

jiF

jnjiT

jnTF

ˆsinˆ cos

ˆ ˆ sinˆ cos

ˆ

mgnTT

nTT

mg

net

net

qq

qq

iF ˆ cos

0sin If

q

q

T

mgnT

net


mg

nT

iF ˆ cos

0sin If

q

q

T

mgnT

net

iclicker exercise:

Assuming T>0, how does the suitcase move along surface? A. It moves at constant

velocity.B. It accelerates.C. Whether it moves or

not depends on magnitude of T.


In presence of friction force:

mg

nT

f

j

iF

ijnTF

ˆsin

ˆ cos

ˆˆ

mgnT

fT

fmg

net

net

q

q


Friction forces

The term “friction” is used to describe the category of forces that oppose motion. One example is surface friction which acts on two touching solid objects. Another example is air friction. There are several reasonable models to quantify these phenomena.

Surface friction:

N

Ff applied

Material-dependent coefficient

Normal force between surfaces

Air friction:

speedhigh at speed lowat

2vKKv

D

K and K’ are materials and shape dependent constants


Models of surface friction forces

(applied force)

surfa

ce fr

ictio

n fo

rce

fs,max=sn

Coefficients s , k depend on the surfaces; usually, s > k


Surface friction models

F-fs = 0 if F < sn=smg

if F>sn=smg , then F-fk=ma (fk= kmg)

mmgFa k

Static friction case:

Kinetic friction case:


mg

f

n

qmg sin q

mg cos q

Consider a stationary block on an incline:

qq

qq

sin 0sin:surface along Forces

cos 0cos:surface tonormal Forces

mgfmgf

mgnmgn


mg

f

n

qmg sin q

mg cos q


What happens when f>fs,max?


mg

f

n

qmg sin q

mg cos q


What happens when f=fs,max? qq

qqqqq

sincosThen

cos Ifsin 0sincos 0cos

max,

mgmg

mgnffmgfmgfmgnmgn

S

SSS

q tanS


V (constant)

iclicker exercise:Suppose you place a box on an inclined surface as shown in the figure and you notice that the box slides down the incline at constant velocity V. Which of the following best explains the phenomenon:

A. There is no net force acting on the box. B. There is a net force acting on the box.

q


V (constant)

q

mg

n

f=kn

Consider a block sliding down an inclined surface; constant velocity case

qqq

qqqq

sincosThen cos If

sin 0sincos 0cos

mgmgmgnf

mgfmgfmgnmgn

K

KK

q tanK


mg

f

n

qmg sin q

mg cos q

Summary

slip about tojust isblock when tanelocityconstant vat movesblock when tan

qq

S

K


A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of q=50o

with the horizontal. s=0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary.

0cos :forces Horizontal0sin :forces Vertical s

NPmgPN

qqf

mg

N

f


0cos :forces Horizontal0sin :forces Vertical s

NPmgPN

qqf

mg

N

f

N 48.57N 72.31

50cos25.050sinN 8.93

cossin :for Solving

0sincoscos

s

s

ooP

mgPP

mgPPPN

qq

qqq


Models of air friction forces

2

air

:ocitieslarger velFor

:s velocitiesmallFor

DvF

bvF

air

mg

bv

mamgbvv

:0 assuming and asdirection up Denoting

mbteb

mgtv

dtdvmmgbv

S

/1)(

:equation aldifferenti olution to


Recall: Uniform circular motion:

animation from http://mathworld.wolfram.com/UniformCircularMotion.html

http://mathworld.wolfram.com/UniformCircularMotion.html


Uniform circular motion – continued

ra ˆ

:ison accelerati lcentripeta theanddirection radial in the

onaccelerati then the, If

2

rv

vvv

c

fi


Uniform circular motion – continued

r

ra

ra

ra

ˆ2

ˆ2

ˆ

2

2

2

rf

rT

rv

c

c

c

Trv 2

In terms of time period T for one cycle:

In terms of the frequency f of complete cycles:πfrv

Tf 2 ;1


Uniform circular motion and Newton’s second law

r

ra

aF

ˆ2

rv

m

c

iclicker exercise:For uniform circular motion

A. Newton’s laws are repealedB. There is a force pointing radially outward from

the circleC. There is a force pointing radially inward to the

circle


http://earthobservatory.nasa.gov/Features/OrbitsCatalog/page1.php

Example of uniform circular motion:


Example of uniform circular motion: Consider the moon in orbit about the Earth

NaMF

smRT

a

s. days.T

mR

kgM

cM

Mc

M

M

20

232

6

8

22

100.2 Law Second sNewton'

/1072.22

10362327 :Moon of period Rotational

1084.3 :Earth ofcenter from Distance

1035.7 :Moon of Mass



ra ˆ2

rv

c

r̂

qq

q

sinsin

:law second sNewton' ofcomponent (radial) Horizontal

0cos:law second sNewton' ofcomponent Vertical

22

Lmv

rmvmaT

mgT

c



mgnmgn 0:law second sNewton' ofcomponent Vertical

grμvr

mvmgμnμ

rmvmaf

sss

c

max

2

2

:condition Maximum

:law second sNewton' ofcomponent (radial) Horizontal


Curved road continued:

hrmim/s.smgrμv

mrμ

grμv

s

s

s

/29113 /358.95.0

35 5.0 :Example

max

max


Mass on a swing:

mg

q T

iclicker exercise:Which of these statements about the tension T in the rope is true?

A. T is the same for all q.B. T is smallest for q0.C. T is largest for q0.

LvmmgT

LvmmgT

2

2

:0For

cos

:rope thealongdirection in the laws sNewton'

q

q

L


Newton’s law in accelerating train car

ga

maθTmgT

q

q

tan

sin :direction Horizontal0cos :direction Vertical


Notion of fictitious forces

iclicker questionA. Fiction is for English class and not for

physics class.B. The concept of fictitious forces is a bad

idea.C. The concept of fictitious forces is

necessary for analyzing certain types of problems.

In analyzing motion in an inertial frame of reference, the notion of “fictitious force” does not appear.


Example of analysis of forces Ferris wheel moving at constant speed v

ac

ac

ctop

ctop

agmn

mamgn

cbottom

cbottom

agmnmamgn


Example of analysis of forces Mass moving in vertical circle

Analysis similar to Ferris wheel except that the speed v varies and the magnitude of the centripetal acceleration varies accordingly.

phy 113 a general physics i 11 am-12:15 p m mwf olin 101 plan for lecture 6:

Documents