A block of mass m begins at rest at the top of a ramp at elevation h with whatev

Question

A block of mass m begins at rest at the top of a ramp at elevation h with whatever PE is associated with that height. The block slides down the ramp over a distance d until it reaches the bottom of the ramp. How much of its original total energy (in J) survives as KE when it reaches the ground? (In other words, the acceleration is not zero like it was in lab and friction does not remove 100% of the original PE. How much of that original energy is left over after the friction does work to remove some?) m = 8.3 kg h=2.2m d =5m mu = 0.3 Theta =36.87?

Explanation / Answer

values of frcition = u.N = u .mgcos@ = 0.3 x 8.3 x 9.81 x cos36.87 = 19.54 J

using work energy theorem ,

work done by friction + work done by gravity = change in K.E.

- f.d + mgdsin@ = K.E. - 0

- 19.54 x 5 + 8.3 x9.81x5 xsin36.87 = K.E.

K.E. = 146.56 J   .................Ans

initially total energy = mgh = 8,3 x 9.81 x 2.2 = 179.13 J

% = 146.56 / 179.13 x 100 = 81.8 %

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