46

30°

W

W||

W

FA

F||

F

FN Equations from Diagram:

W|| = F||

FN = F + W

m = 5

W = 49

W= 42.4

W|| = 24.5

cos30 = F||

FA

cos30 = 24.5

FA

Same as W||

FA = 28.3 N

FN = F + W

FN = 14.2 + 42.4

FN = 56.6 N

50

T

W

T - W = FNET

T - 5(9.8) = 5(3)

T = 64 N

53FN

W

Ff

FN = W

Ff = FNET

Find d:

vi = 7

vf = 0

d = ?

a =

Find a:Find Ff:

same as FNET FNET = m a

32.3 = 65.8a

a = .491

Ff = FN

Ff = .05(645)

Ff = 32.3.491

vf2 = vi

2 + 2ad

02 = 72 + 2(.491)d

d = 49.9 m

55

30°

W

W||

W

FN

Ff W|| - Ff = FNET

FN = W

m = 3

W=29.4

W=25.5

W||= 14.7

A.

vi =0

d = 2

t = 1.5

a = ?

d = vit + ½ at2

2 = ½ a(1.5)2

a = 1.78 m/s2

B.

W|| - Ff = FNET

14.7 – Ff = 3(1.78)

Ff = 9.36 N Ff = FN

9.36 = (25.5)

= .367

C. Already found this !

9.36 N

D. vf2 = vi

2 + 2ad

vf2 = 2(1.78)2

vf = 2.67 m/s

56 Ff

W

W – Ff = FNET

Find vf :Find a :Find FNET :

vi = 0

vf = ?

d = 25

a =

FNET = maW – Ff = FNET

75(9.8) – 95 = FNET

FNET = 640

640 = 75a

a = 8.53 8.53

vf2 = vi

2 + 2ad

vf2 = 2(8.53)(25)

vf = 20.7 m/s

59

35°

W

W||

W

FN

FA

Ff W|| = Ff

W + FA = FN

m = 3

W = 29.4

W= 24.1

W|| = 16.9

Find FA :

W + FA = FN

Find FA :

Ff = FN

16.9 = .300FN

FN = 56.3

24.1 + FA = 56.3

FA = 32.2 N

61

°

W

W||

W

FN

FA W|| = FA

W = FN

sin = W||

W

sin = 300

12200

Same as FA

= 1.4°

63

2 34

180

A. Whole:

W

FN

FA

FNET = ma

180 = 9a

a = 20 m/s2 For ALL blocks

B.

Resultant force is NET force

FNET = ma= 2(20)

= 40 N

For m1

FNET = ma= 3(20)

= 60 N

For m2

FNET = ma= 4(20)

= 80 N

For m3

C. Between m1 and m2:

W

FN

Ffrom m1

FNET = ma= 7(20)

= 140 N

D. Between m2 and m3 :

80 N…..it is the NET force on m3