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Question Number 119661 by aurpeyz last updated on 26/Oct/20

point A is at the bottom of a rough   plane which is inclined at an angle   Θ to the horizontal. A body of mass   m is projected from A along and end   up a line of greatest slope (along the  plane). the cofficient of friction between  the body and the plane is ϕ. it then   comes to rest at point B at a distance X   from A. obtain the expression for  (a) the workdone against friction  when the body moves from A to B  and back to A  (ii) initial speed of the body  (iii) the speed of the body on its   return to A

$${point}\:{A}\:{is}\:{at}\:{the}\:{bottom}\:{of}\:{a}\:{rough}\: \\ $$$${plane}\:{which}\:{is}\:{inclined}\:{at}\:{an}\:{angle}\: \\ $$$$\Theta\:{to}\:{the}\:{horizontal}.\:{A}\:{body}\:{of}\:{mass}\: \\ $$$${m}\:{is}\:{projected}\:{from}\:{A}\:{along}\:{and}\:{end}\: \\ $$$${up}\:{a}\:{line}\:{of}\:{greatest}\:{slope}\:\left({along}\:{the}\right. \\ $$$$\left.{plane}\right).\:{the}\:{cofficient}\:{of}\:{friction}\:{between} \\ $$$${the}\:{body}\:{and}\:{the}\:{plane}\:{is}\:\varphi.\:{it}\:{then}\: \\ $$$${comes}\:{to}\:{rest}\:{at}\:{point}\:{B}\:{at}\:{a}\:{distance}\:{X}\: \\ $$$${from}\:{A}.\:{obtain}\:{the}\:{expression}\:{for} \\ $$$$\left({a}\right)\:{the}\:{workdone}\:{against}\:{friction} \\ $$$${when}\:{the}\:{body}\:{moves}\:{from}\:{A}\:{to}\:{B} \\ $$$${and}\:{back}\:{to}\:{A} \\ $$$$\left({ii}\right)\:{initial}\:{speed}\:{of}\:{the}\:{body} \\ $$$$\left({iii}\right)\:{the}\:{speed}\:{of}\:{the}\:{body}\:{on}\:{its}\: \\ $$$${return}\:{to}\:{A} \\ $$

Commented by aurpeyz last updated on 26/Oct/20

pls help

$${pls}\:{help} \\ $$

Commented by aurpeyz last updated on 28/Oct/20

pls help

$${pls}\:{help} \\ $$

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