Chapter 3-Acceleration and Newton Second Law of Motion

8/11/2019 Chapter 3-Acceleration and Newton Second Law of Motion

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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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3

,

. , ,

( ).


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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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3.11

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F. 3.39 , ; .

1= 26.0 2= 42.0 , ?

3.11


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55

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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

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Chapter 3-Acceleration and Newton Second Law of Motion