You release a block from the top of a long, slippery inclined plane of length l

Question

You release a block from the top of a long, slippery inclined plane of length l that makes an angle with the horizontal. The magnitude of the block's acceleration is gsin() .

For an x axis pointing down the incline and having its origin at the release position, derive an expression for the potential energy of the block-Earth system as a function of x. Suppose that the gravitational potential energy is measured relative to the ground at the bottom of the incline, UG(x=l)=0.

Express your answer in terms of g and the variables m, l, x, and .

UG= ?

Explanation / Answer

Work done by gravity at position x = mg sin@ *x = mgxsin@

PE = - work done

PE = - mgx sin@ ...................Ans

For botttom,

x = L

PE = - mgLsin@

B) Using energy conservation ,

initial PE +KE = final PE +KE

0 + 0 = - mgLsin@ + mv^2 /2

v = sqrt(2gLsin@)

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