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# Energy on Ramp with Friction

APPH12-VWGLJV

A box is given an initial push up a ramp that is inclined at angle $\alpha$ above the horizontal, and then allowed to slide freely up the ramp until it stops at a maximum height $H$, measured relative to the box's starting height. The box's speed at the base of the ramp is $V$, and the coefficient of kinetic friction between the box and ramp is $\mu$.

Which one of the following is a correct conservation of energy equation for this situation?

A

$\dfrac { 1 }{ 2 } m{ V }^{ 2 }+\dfrac { \mu mgH\sin { \alpha } }{ \cos { \alpha } } =mgH$

B

$\dfrac { 1 }{ 2 } m{ V }^{ 2 }-\mu mgH\cos { \alpha } =mgH$

C

$\dfrac { 1 }{ 2 } m{ V }^{ 2 }+\mu mgH\sin { \alpha } =mgH$

D

$\dfrac { 1 }{ 2 } m{ V }^{ 2 }-\dfrac { \mu mgH\cos { \alpha } }{ \sin { \alpha } } =mgH$