The-ratio-of-acceleration-of-points-A-B-and-C-is-assume-all-surfaces-are-smooth-pulley-and-strings-are-light-

Question Number 24772 by Tinkutara last updated on 25/Nov/17

The ratio of acceleration of points A,

B and C is [assume all surfaces are

smooth, pulley and strings are light]

Commented by Tinkutara last updated on 25/Nov/17

Commented by mrW1 last updated on 26/Nov/17

I t h i n k B a n d C c a n m o v e i n d e p e n d e n t l y

f r o m A, t h e r e f o r e t h e r e i s n o c e r t a i n

r a t i o b e t w e e n a_{A} a n d a_{B} .

Commented by Tinkutara last updated on 26/Nov/17

Answer is wrong .

Why a_{B} = a_{C} = \frac{9 F}{m} ?

Commented by mrW1 last updated on 26/Nov/17

a_{A} = \frac{3 F}{m}

a_{F} = 3 a_{A} = \frac{9 F}{m} (a c c e l e r a t i o n o f t h e e n d o f s t r i n g)

a_{B} = a_{C} = 0

Commented by Tinkutara last updated on 26/Nov/17

B u t a n s w e r i s s t i l l w r o n g a s r a t i o i s

i n t e g e r .

Commented by mrW1 last updated on 26/Nov/17

T h i s i s I t h i n k t h e r i g h t a n s w e r .

Commented by ajfour last updated on 26/Nov/17

I s B a r o p e p o i n t o r c e n t r e o f

p u l l e y ?

Commented by mrW1 last updated on 26/Nov/17

B (a s w e l l a s C) i s c e n t e r o f p u l l e y .

Commented by ajfour last updated on 26/Nov/17

3 x + 2 l + 3 y = c o n s t a n t

3 (a_{C} - a_{A}) - 3 a_{B} + a_{F} = 0 \dots . (i)

{F v}_{F} = {m v}_{A} a_{A}

\Rightarrow {F a}_{F} = {m a}_{A}^{2} + 0

F u r t h e r 3 F = {m a}_{A}

a_{A} = \frac{3 F}{m}

\Rightarrow a_{F} = 3 a_{A} = \frac{9 F}{m} .

N o w f r o m (i) :

a_{C} = a_{B} = (w h a t e v e r, d e p e n d s o n

m a s s o f s m a l l p u l l e y s) .

Commented by Tinkutara last updated on 26/Nov/17

A n s w e r i s 3 : 1 : 1

Commented by jota+ last updated on 26/Nov/17

L a r e s u l t a n t e s o b r e e l s i s t e m a B

y C i s z e r o . 2 F - 2 F = 0

\Rightarrow a_{B} = a_{C} = 0

Commented by mrW1 last updated on 26/Nov/17

A n s w e r 3 : 1 : 1 i s w r o n g i n e a c h c a s e,

t h a t w u r d e m e a n a_{A} = 3 a_{B} = 3 a_{C} .

B u t t h i s i s w r o n g e v e n i f B a n d C

a r e t h e r o p e p o i n t s . I f B a n d C a r e

t h e p o i n t s o n t h e r o p e, t h e n t h e

a n s w e r s h o u l d b e 1 : 3 : 3 w i t h

a_{A} = \frac{3 F}{m}

a_{B} = a_{C} = 3 a_{A} = \frac{9 F}{m}

T h i s w a s m y o r i g i n a l a n s w e r .

I f B a n d C a r e t h e c e n t e r o f p u l l e y,

t h e n a_{A} : a_{B} : a_{C} = u n c e r t a i n .

Commented by Tinkutara last updated on 26/Nov/17

T h a n k s S i r! I w i l l c o n f i r m .