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C GH C, . .
Chapter 3
UNIT 5Section 3.1
Section 3.2Section 3.3
Section 3.4
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POSITION AND DISPLACEMENT
2
Introduction to Newtons Second Law of Motion
In the previous chapter 2, we concentrated on situations in
which the net force acting on an object is zero. When anonzero net force acts on an object, the velocity changes.
Newtons second law of motion (presented in Section 3.3)tells us how the net force and the objects mass determine the
change in velocity.
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POSITION AND DISPLACEMENT
3
,
. , ,
( ).
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POSITION AND DISPLACEMENT
4
.
D .
.
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positioninitial=o
x
r
positionfinal=xr
ntdisplaceme==
o
xxx
rrr
Displacement is a vector quantity.
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m0.2=o
x
r
m0.7=xr
m0.5=xr
m0.5m2.0m7.0 === oxxxrrr
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Example 3.2
7
C, C
27 18 ,
17 G, 13 48
C.
?
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Example 3.2
8
A
A
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Example 3.2
9
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Example 3.2
10
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Example 3.2
11
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Speed and Velocity
Average speed is the distance traveled divided by the timerequired to cover the distance.
timeElapsed
DistancespeedAverage =
SI units for speed: meters per second (m/s)
and speed is a scalar quantity.
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Average velocity is the displacement divided by the elapsed
time.
timeElapsedntDisplacemevelocityAverage =
ttt o
o
=
=
xxx
v
rrr
r
Speed and Velocity
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14
.
,
. H,
.
Speed and Velocity
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The instantaneous velocity indicates how fast
an object moves and the direction of motion at each
instant of time.
tt =
xv
r
r
0lim
Velocity
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16
Velocity
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17
Velocity
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ExampleAndy Green in the carThrustSSCset a world record of 341.1 m/s in 1997.To establish such a record, the driver makes two runs through the course,one in each direction, to nullify wind effects. From the data, calculate theaverage velocity for each run.
Velocity
sm5.339s4.740
m1609+=
+=
=
t
x
v
r
r
sm7.342s4.695m1609 ==
=t
xv
r
r
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Example 3.4
19
/ = 40 .
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Example 3.4
20
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VELOCITY
21
.
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ACCELERATION AND NEWTONS SECOND
LAW OF MOTION
22
,
:
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The notion of acceleration emerges when a change in velocity is
combined with the time during which the change occurs.
ACCELERATION
ttto
o
=
=
vvv
a
rrr
r
DEFINITION OF AVERAGE ACCELERATION
Average Acceleration is the rate at which the velocity changes
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Example 3 Acceleration and Increasing Velocity
Determine the average acceleration of the plane.
sm0=o
v
r
hkm260=vr
s0=ot s29=t
s
hkm0.9
s0s29
hkm0hkm260+=
=
=
o
o
tt
vv
a
rr
r
ACCELERATION
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ACCELERATION
Acceleration and increasing velocity
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Acceleration and Decreasing
Velocity
2sm0.5s9s12
sm28sm13=
=
=
o
o
tt
vv
a
rr
r
ACCELERATION
Whenever the acceleration
and velocity vectors have
opposite directions, the objectslows down and is said to be
deccelerating.
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27
F
:
ACCELERATION
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28
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2sm6s2
sm12Slope +=
+=
=
t
v
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Example 3.6
31
A 8.94 /; 120.0 15.0
7.15 /.
() ?
() 120.0 ?
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Example 3.6
32
1.79 / (=8.94 /7.15/).
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Example 3.6
33
()
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Example 3.6
34
()
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Example 3.6
35
()
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36
(),
().
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37
(/)/ = /2.
, ,
1 1 1 /2 :1 = 1 /2
NEWTONS SECOND LAW OF MOTION
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NEWTON S SECOND LAW OF MOTION
38
.
. .
.
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39
D ( ) .
.
.
D FBD .
C .
, (
) .
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40
F .
.
.
3 4 APPLYING NEWTONS LAWS
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3.4 APPLYING NEWTON S LAWS
41
.
E 3.10,
.
,
; , .
, ,
.
3 8
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3.8
42
B , .
40.0 .
36.0 B 65.0 .
3 8
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3.8
43
() ?
()
= 0.13, .
() B
65.0 40.0 ?() ,
0.5 /?
3 8
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3.8
44
()
3 8
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3.8
45
()
()
0.3 /2 +.
()
3 9
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3.9
46
A 1.0 30.0
.
,
0.90 ? .
3 9
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3.9
47
3 9
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3.9
48
4.4 / 30.0 .
3 10
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3.10
49
A ,
90.0 . 15.0
/ 5.00 .
A
,
?
.
3 10
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3.10
50
3 10
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3.10
51
3 10
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3.10
52
3 11
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53
F. 3.39 , ; .
1= 26.0 2= 42.0 , ?
3.11
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3.11
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Additional examples - A
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Two different boxes of masses M = 125 kg and m = 45 kg are sliding
down a rough surface inclined = 35, as shown in the figure below. If
the coefficients of kinetic friction between the big and small boxes and
the inclined surface are 0.3 and 0.5 respectively, calculate theacceleration of the two boxes and the contact force between them.
dd t o a e a p es
Additional examples - B
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Two objects with mass m1 = 3 kg and m2 = 2 kg are connected by amassless string that runs over an ideal pulley moves on two frictionless
surfaces, as shown in the figure below. The inclined surface at the left is
tilted at an angle 1 = 45 with respect to the horizontal, and surface at
the right at 2 = 60. Calculate the:(i) Magnitude of the acceleration of the two objects, and
(ii) Magnitude of the tension on the string.
p