A mass of 6kg lies on an inclined plane which is smooth at angle θ to the horizontal where sin θ= (1/3).if it is connected to another mass 8kg by the same inelastic string passing over a smooth fixed pulley at the top of the plane.the partices are released from rest ,Find a) the acceleration of each mass b) the tension in the string c) the speed of the masses after 4seconds d) the distanced covered with this time in (c) above by the masses. 2017 CGCEB paper 3 Mechanics a/v


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Question Number 55306 by Rio Mike last updated on 21/Feb/19

$A m a s s o f 6 k g l i e s o n a n i n c l i n e d p l a n e$ $w h i c h i s s m o o t h a t a n g l e θ t o t h e h o r i z o n t a l$ $w h e r e \sin θ = \frac{1}{3} . i f i t i s c o n n e c t e d t o$ $a n o t h e r m a s s 8 k g b y t h e s a m e i n e l a s t i c s t r i n g$ $p a s s i n g o v e r a s m o o t h f i x e d p u l l e y$ $a t t h e t o p o f t h e p l a n e . t h e p a r t i c e s a r e$ $r e l e a s e d f r o m r e s t, F i n d$ $a) t h e a c c e l e r a t i o n o f e a c h m a s s$ $b) t h e t e n s i o n i n t h e s t r i n g$ $c) t h e s p e e d o f t h e m a s s e s a f t e r 4 s e c o n d s$ $d) t h e d i s t a n c e d c o v e r e d w i t h t h i s t i m e$ $i n (c) a b o v e b y t h e m a s s e s .$ $2017 C G C E B p a p e r 3 M e c h a n i c s a / v$
	Answered by tanmay.chaudhury50@gmail.com last updated on 21/Feb/19

	$8 \times 10 - T = 8 a [$ $T - 6 \times 10 \times \frac{1}{3} = 6 a$ $14 a = 60 a = \frac{30}{7} m / {s e c}^{2} \to f o r b o t h m a s s$ $T = 80 - 8 \times \frac{30}{7} = 80 (1 - \frac{3}{7})$ $T = \frac{320}{7} N$ $v = 0 + \frac{30}{7} \times 4 = \frac{120}{7} \to f o r b o t h m a s s$ $s = \frac{1}{2} \times \frac{30}{7} \times 4^{2} = \frac{240}{7} m e t e r$
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