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I was trying to work out a problem on conservation of energy and am totally stuck. Was hoping someone could help.... the problem was this...

A 38 kg block slides with an initial speed of 7 m/s up a ramp inclined at an angle of 35o with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.5. Use energy conservation to find the distance the block slides before coming to rest.

I was working with the assumption that at the end of the climb,

PE = KE + Wf

where, PE = potential energy

KE = kinetic energy

Wf = work done by friction = coefficient * Normal force

Reason I get stuck is that there is no d (displacement on slope) or h (height of block at the end of motion). I tried solving one for the other by using h/d = sin theta.... but I don't think it's right.

******EDITED PART STARTS*******

Here's what i had done:

PE = KE - Wf (minus cuz going up the slope)

mgh = mv2 - (F*d) (F = friction_coeff * m * g * cos theta)

dividing both sides by m*g*d I got....

h/d = (v2/dg) - (F/mg)

but, h/d = sin theta

so,

v2/dg = (F/mg) + sin theta

then I solved for d... and got an answer of 5.1 m. However this was wrong!

******EDITED PART ENDS******

And I've spent an hour on this and am totally frustrated and thus useless ... any and all assistance/clue/guidance will be totally appreciated.

Thanks.

- O

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# Conservation of energy of sliding block

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