First slide

Work

Question

A particle is moving with kinetic Energy E, straight up an inclined plane with an angle $α$ , the coefficient of friction being $μ$ . The work done against friction before the particle comes to rest is,

Moderate

A

$\frac{E μ \cos α}{\sin α + (\cos α) μ}$
B

$\frac{E \cos α}{\sin α + μ \cos α}$
C

$\frac{E}{\sin α + μ \cos α}$
D

$\frac{E}{g (\sin α + μ \cos α)}$

Solution

$g i v e n K E = E i s u t i l i z e d i n w o r k d o n e i n o v e r c o m i n g f r i c t i o n a n d c l i m b i n g u p t h e i n c l i n e a p p l y p r i n c i p l e o f c o n s e r v a t i o n o f e n e r g y K E = w o r k_{f r i c t i o n} + P E E = f . s + m g s \sin α h e r e f = μ m g \cos α = f o r c e o f f r i c t i o n; s i s d i s p l a c e m e n t u p t h e i n c l i n e p l a n e E = (μ m g \cos α) . s + m g s \sin α s = \frac{E}{m g (μ \cos α + \sin α)} w o r k d o n e a g a i n s t f r i c t i o n = f . s = (μ m g \cos α) . \frac{E}{m g (μ \cos α + \sin α)} w o r k d o n e a g a i n s t f r i c t i o n = \frac{μ E \cos α}{(μ \cos α + \sin α)}$

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