Dynamics

OBJECTIVES:

Some important kinds of Forces such as ; NORMAL & FRICTION Forces

In this chapter we will learn :

The Laws of Motion

How to solve dynamics problems by the Laws of Motion

DYNAMICS

is the relation between FORCE & MOTION

THE KINDS OF FORCES

1. NORMAL Force:

is REACTION Force, perpendicular to the surface that the action force is applied

FORCE: is the Effect that can destroy, stop or move the objects.

Since it shows a DIRECTION. Then it is a VECTOR Quantity.

FRICTIONAL FORCE • Frictional force: It is an important force which only acts when two objects are

touching and are applying force to one another.• It is a force that slows down moving objects and brings them to rest. • It always acts in a direction opposite to the direction of the force applied to the

object. • Walking is possible only on a frictional surface.• Water also applies a frictional force to the objects moving in it.• Frictional force does not depend on the area of the rubbing surfaces. The

frictional force between the object and the table depends on two factors;

a. The weight of the object.

b. The roughness of the surfaces rubbing together.

2. FRICTION Force:

is REACTION Force, formed in opposite direction to the action force applied.

fF

extF

maxfF

MotionNo

fFextF

maxfF

Between two surface, there is a maximum value of Friction Force.

maxfF

MovetoadyRe

Friction

Kinetic

Friction

Static

Let us write an equation about this maximum friction force between two surface.

NFf .max

NFf max

We call this constant as the coefficient of friction, µ between two surface

maxfextNET FFF

constN

Ff max

Ex: Find the friction force in both case.

NFf .max mgW

NF

FWFf .max

N

F

mgW FWN

FWFf .max FWN

3. TENSION Force:

4. GRAVITATIONAL Force:

5. MAGNETIC Force:

6. ELECTROSTATIC Force:

7. NUCLEAR Force:

is ACTION-REACTION Force, formed along stretch Force applied.

is Natural Attractive Field Force, between two bodies that appears as the WEIGHT.

gmW .m

Fg G

GF

WFG

kgmmNmgW 1010100

GF GF GF

We define the Gravitational Field as;

Planet Field Strength Mass Weight

MercuryVenusEarthMoonMarsJupiterSaturnUranusNeptunePluto

3,78 N/kg8,94 N/kg10 N/kg1,7 N/kg3,79 N/kg25,4 N/kg10,7 N/kg9,2 N/kg12 N/kg0,3 N/kg

40 kg40 kg40 kg40 kg40 kg40 kg40 kg40 kg40 kg40 kg

XXXXXXXXXX

==========

151 N358 N400 N67 N152 N1067N428 N368 N480 N12 N

Ex: What is the weight of an object on the Moon which has the weight on Earth as 100N ?

NmgW 177,1.10

.

.

.

LAWS OF MOTION

I-) INERTIA PRINCIPLE:

INERTIA: is the tendency to keep the initial position

II-) ACTION PRINCIPLE:

III-) ACTION-REACTION PRINCIPLE:

PRINCIPLE: If the NET FORCE is ZERO on an object ; Either the object stops or moves steadily (with constant velocity)

If the NET FORCE is not ZERO on an object ;Either the object will be accelerated or decelerated

If an object applies a Force on another object. The Other One replies with the same Force in opposite direction

amFNET .

a2

aF NET NETFm

NETF2m

a

m NETF3 a3

consta

FNET )(mmass

INCLINED PLANE:RFW sin.

Wx

y

sin.W

N

cos.W

fF

cos.mgFf

Object is sliding down.

Along y-axis, There is no motion.

Along x-axis, There is motion.

0netF

amFnet

amFWFFF ffRnet sin.

0cos. WNNFf .

cosmgN

mamgmg cos.sin

0

cossin. ga

If there is no FRICTION, then take;

sin.ga

LIFT PROBLEMS:

T

ficF

a

.ficFWT

0NetF

mamgT

maFNet

0. ficFWT

agmT

mamgT

amWT .

agmT

mgW

TficF

a

.ficFWT

0NetF

mamgT

maFNet

0. ficFWT

agmT

mamgT

amWT .

agmT

mgW

Let us look at the cases by both the observers inside the Lift and outside the Lift

A- The Lift accelerated upward or decelerated downward ;

B- The Lift accelerated downward or decelerated upward ;

Apparent Weight

W = m(g+a) W = m(g-a) WeightlessW = mg

m=10 kg

Ex.: What is the acceleration of the object, a=?

5,0

fF N100F

a

N

W

N

N

50

100.5,0

0NetF

Ex.: A force of 10N is applied on the mass of the 2kg with and angle of 370. If the coefficient of friction between mass and surface is 0.1, what is the acceleration of the mass in m/s2 ?

NFf

0WN Along y-axis; There is no MOTION, ay=0

amFNet

g

mWN

Along x-axis; There is MOTION, a=ax

amFF f

N100N

2/5 sma

akgNN .1050100

m=2 kg

1,0

fF

a

N

W

N

N

4,1

14.1,0

0NetF

NFf

0WFN Y Along y-axis; There is no MOTION, ay=0

amFNet

YFWN

Along x-axis; There is MOTION, a=ax

amFF fX

NNN 14620N

2/3,3 sma akgNN .24,18

XF

YF

N10F

037

0Y .sin37FF

0X .cos37FF

NN 6.0,601

NN 8.0,801

m1=3kg

Ex.: Two masses which are contact with each other are pushed by a force of 20 N. What force does the mass A apply to the mass B when coefficient of friction between the masses and the surface; µ=0 and µ=0.1?

1fF

N20F

a

1N

1W

0NetF

NNNFf 330.1,011

N03WN 11

Along y-axis; There is no MOTION, ay=0

amF TNet

Along x-axis; There is MOTION, a=ax

ammmFFFF fff

.321321

2/2 sma akgNNNN .)202030()404060(280

m2=2kg

2fF

2N

2W

R

N02WN 22

NNNFf 220.1,022

amF TNet

ammFFF ff

2121

2/3 sma akgNN .5520

For Reaction Force, R; Choose one of the masses, ex; m2

For Reaction Force, R; Choose one of the masses, ex; m2

amRFNet

2 amFRF fNet

22

NsmkgR 8/4.2 2

NsmkgNR 8/3.22 2

Ex.: Three masses are connected with ropes. A force of 280 N acted on the masses as shown in the figure. Find the tensions in the rope T1 ,T2 .

N280F

2,0

kgm 203 kgm 202 kgm 301 1T

a1N

1W1fF

3fF

2fF

3W

3N

2N

2W

2T

NNNFf 60300.2,011

NNNFf 40200.2,022

NNNFf 40200.2,033

system; allFor

amFNet

3amFT f

.332

22 /2.2040 smkgNT

; mFor 3

NT 802

amFNet

2 amFTT f

.2221

21 /2.204080 smkgNNT

; mFor 2

NT 2002

amF TNet

ammF

21

2/4 sma

akgN .520

42NT

?F

a

kgm 32

kgm 51

Ex.: Two masses are connected to each other as shown in figure are pulled up by force F. If the tension in the cord is 42N what is the force F?

1W

2W

amFNet

2

amWT

.22 akgNN .33042

; mFor 2

2/4 sma

amF TNet

ammWWF

.2121

system; allFor

2/4.353050 smkgkgNNF

NF 112

Ex. ( Atwood Machine) : When the system is released , find the tension in the rope in N, T= ?

kgm 52 kgm 151

1W

2W

T T

a

amF TNet

ammWW

.2121

2/5 sma akgkgNN ).515(50150

system; allFor

amFNet

1

amTW

.11

; mFor 1

NT 75

2/5.15150 smkgTN

Ex.: Find acceleration of the system and T1 & T2 When the coefficient of friction between 10kg of mass and the surface,µ=0 and µ=0.1?

kgm 61 kgm 42

kgm 103 1T

1T

2T

2T

1W

2W

a

amF TNet

ammmWW

.32121

2/1 sma akgkgkgNN ).1046(4060

system; allFor

amFNet

1

amTW

.111

; mFor 1

NT 541

2/1.660 smkgTN

amFNet

2

amWT

.222

; mFor 2

NT 442

22 /1.440 smkgT

Ex.: When the system is released, what is the Acceleration of the system. The coefficient of friction is µ=0,1.

kgm 22

kgm 21

1W

2W

037

01 37sin.W

01 37cos.W fF

a

T

N

N126,0.10.2

NWN 168,0.10.237cos. 01

NNN 6,116.1,0

N20

amF TNet

ammFWW f

.37sin. 21

012

2/6,1 sma akgkgNNN ).22(6,11220

system; allFor

Ex.: Find the velocities of the objects K and L shown in figure .3 seconds later, after they are released.

12 2TT

1a

kgm 82

kgm 41

1,0

2a

fF

12 2aa

2W

2T

1T

1T

1T

11amFNet

111 .amFT f

; mFor 1

11 44 aT

22amFNet

2222 .amTW

; mFor 2

22 .880 aT

N

N

NFf

4

40.1,0

N

1W

11 2.8280 aT 11 .840 aT

22 /6 sma 2

1

1

/3

3612

sma

a

tav .22 tav .11 ssm 3./6 2ssm 3./3 2

sm /18sm /9

Ex.: In the figure the coefficient of kinetic friction is µ for all interacting surfaces. Find the accelerations of the blocks a.

F

2m

1m

a 1N

1W 1fF

1fF

T

T

2N

2W

a

amFNet

1amFT f

.11

; mFor 1

amFNet

2amFFTF ff

.212

; mFor 2

2fF

111 10mNFf

2122 10 mmNFf

gmWN 111 gmmWWN 21212

amFFamFF fff .21211

amgmgmmamgmF .212111

amgmgmgmamgmF .212111 amgmamgmF .3 2211

ammgmmF .3 2121

g

mm

mmFa

21

213

Ex.: The objects K and L are released in a frictionless system as shown in figure. Find the tension T on the rope which joins the objects K and L . mK=mL=1kg

aT

037

K

053

L

KW

053sin.KW

053cos.KW

LW

037sin.LW 037cos.LW

KN

LN

amF TNet

ammWW LKLK

.37sin53sin 00

2/1 sma akgkg ).11(6,0.108,0.10

system; allFor

1. What is Force? How many kinds of Forces are there?2. Why do we need to use the kind of ``NORMAL FORCE``?3. What are the factors that the force of friction depends on?2. What is the difference between uniform motion and uniformly

accelerated motion?3. Driving on an icy high way is particularly dangerous. Why?4. What is INERTIA and its Principle? Give some examples5. You hit a ball with your foot. Since the forces are F and –F

can you say the total force is zero? Then why does the ball start to move?

6. The x-component of the projected objects is always constant , why?

7. Mostly which Law of Motion is used to solve Dynamics Problems?

8. What is Atwood Machine? And how do we find the acceleration of it?

9. Can we feel ``Weightlessness`` on Earth? How?

CHECKING OF UNDERSTANDING (HOMEWORK)

The Answers of them should be placed just after this Chapter before the Next Chapter.

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