A-block-is-released-from-rest-at-the-top-of-a-frictionless-incline-plane-16-00m-long-It-reaches-the-bottom-4-0s-later-A-second-block-is-projected-up-the-plane-from-the-bottom-at-the-instant-the-first-

Question Number 24178 by NECx last updated on 13/Nov/17

A b l o c k i s r e l e a s e d f r o m r e s t a t t h e

t o p o f a f r i c t i o n l e s s i n c l i n e

p l a n e 16.00 m l o n g . I t r e a c h e s t h e

b o t t o m 4.0 s l a t e r . A s e c o n d b l o c k

i s p r o j e c t e d u p t h e p l a n e f r o m t h e

b o t t o m a t t h e i n s t a n t t h e f i r s t o n e

i s r e l e a s e d i n s u c h a w a y t h a t i t

r e t u r n s t o t h e b o t t o m s i m u l t a n e o u s l y

w i t h t h e f i r s t b l o c k . F i n d :

a) t h e a c c e l e r a t i o n o f e a c h b l o c k

o n t h e i n c l i n e p l a n e

b) t h e i n i t i a l v e l o c i t y o f t h e f i r s t

b l o c k .

c) h o w f a r u p t h e i n c l i n e p l a n e

d i d t h e s e c o n d b l o c k t r a v e l .

d) W h a t a n g l e d o e s t h e p l a n e m a k e s

w i t h t h e h o r i z o n t a l .

(g = 10 m / s^{2})

Commented by NECx last updated on 14/Nov/17

p l e a s e I v e i s s u e s w i t h t h i s q u e s t i o n

Commented by ajfour last updated on 14/Nov/17

Commented by ajfour last updated on 14/Nov/17

L e t b l o c k B w a s p r o j e c t e d w i t h

i n i t i a l v e l o c i t y u .

s_{A} = l a n d s_{B} = 0, i n a t i m e o f 4 s .

\Rightarrow \frac{1}{2} (g \sin θ) t^{2} = l a n d

- u t + \frac{1}{2} (g \sin θ) t^{2} = 0

o r \Rightarrow 8 g \sin θ = 16

\sin θ = \frac{1}{5} o r θ = \sin^{- 1} (\frac{1}{5})

\Rightarrow 4 u = 16

u = 4 m / s .

0 = u^{2} + 2 (g \sin θ) s_{u p t h e i n c l i n e}

s_{u p t h e i n c l i n e} = \frac{u^{2}}{2 g \sin θ} = \frac{16 \times 5}{20 \times 1} = 4 m .

A c c e l e r a t i o n o f b o t h b l o c k s d o w n

t h e i n c l i n e i s m g \sin θ / m = g \sin θ

A s a l r e a d y f o u n d a b o v e \sin θ = \frac{1}{5}

s o a n g l e o f i n c l i n e i s θ = \sin^{- 1} (\frac{1}{5}) .

Commented by NECx last updated on 14/Nov/17

w o w \dots . T h a n k s

Commented by NECx last updated on 14/Nov/17

o h \dots . . i d o n t t h i n k {y o u}^{'} v e c o m p l e t e d

i t . I t r e m a i n s (a) (c) n (d)

Commented by NECx last updated on 15/Nov/17

t h a n k s b o s s .

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