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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.