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,

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,

Infinity Learn · Accepted Answer

given $$KE$$$$=E$$  is utilized in work done in overcoming friction and climbing up the incline apply principle of conservation of energy $$KE$$$$=workfriction+$$$$PE$$ $$E=f$$.$$s+mgssin$$α here f $$=$$μmgcosα $$=force$$ of friction; s is displacement up the incline plane $$E=($$μmgcosα$$)$$.s $$+mgssin$$α $$s=Emg($$μ$$cos$$α$$+$$$$sin$$α$$)$$ work done against friction $$=f$$.$$s=($$μmgcosα$$)$$.$$Emg($$μ$$cos$$α$$+$$$$sin$$α$$)$$ work done against friction $$=$$μEcosα$$($$μ$$cos$$α$$+$$$$sin$$α$$)$$

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,

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