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F = ma

F12

F21

F21 = F12

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F = 0

Fx = 0

Fy = T Fg = 0 T = Fg

Fy = n Fg = 0 n = Fg

Fy = T = max ax =

T

m

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Fy = mg R

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x = g kv2v2

mx = mg mkv2 x = g kv2

v dvdx

= g kv2v

gkv2dv =

dx

12k ln(g kv2) = x + C,

v2 = gk

(1 e2kx)

v =

gk

(1 e2kh)

v2 = U2 2gR2( 1R 1

x)

9.8ms2

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a =dv

dt= k

x2

g = kR2 k = gR2

dv

dt

=

gR2

x2

vdv

dx= gR

2

x2

vdv = gR

2

x2dx

v2

2= gR2

1

x

+ C

U2

2= gR2( 1

R) + C C = U

2

2+ gR

v2 = U2 2gR2( 1R 1

x)

U2 = 2gR2(1

R 1

x)

x =2gR2

2gR

U2

x

2gR U2 0

U =

2gR 11.2kms1

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a = k(1

v2), k > 0

v210 ms2U ms1

v =10U

10+Ut ms1x = 10ln(1 + Ut10 ) m

v + v3

x = arctan( Qv1+Qv )

t = 12 ln(Q2(1+v2)v2(1+Q2) v

2

t

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Fx = Fcos

Fy = Fsin

= ddt

v = r at = ddt =

dd

12

2 = dd

=

ac = r2 = v2

r

Fc = m v2

r = mr T = 2

T = mv2

r= (3)(

16

2) = 8 N

mv2

r= 147 v =

147

r

m= 7

2

v = r = 7

2 = 722

rad/s

=7

2

4rev/s

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P F = 0

mg N =mv2

r

N = mg mv2

r= 3400 N

mg =mv2

r v2 = gr

ms2

F = kmM

r2

mg = kmM

R2 k = gR

2

M

F =mgR2

r2= mr2

=2

T 7.3 105 rad/s

r3 =gR2

2=

(9.8)(6.4 106)2(7.3 105)2 = 7.53 10

22 r = 4.22 107 m

v = r = (4.22 107)(7.3 105) = 3000 ms1

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Horizontally : Tsin = mr2

V ertically : Tcos = mg

l2 = r2 + h2

r = lsinh = lcos

T = ml2 tam = r2

g= v

2

gr

tan = rh

=

gh

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F + mgsin =mv2

rcos

Nmgcos = mv2

rsin

mv2

r= Fcos + Nsin

mg = Ncos Fsin

F = 0

tan =v2

gr

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F + mgsin =

mv2

r cos

tan =v2

gr=

13.42

(9.8)(50) = 20.1

T = 2

hg

40