Starting from rest, a 10.2 kg block slides 2.90 m down a frictionless ramp (inclined at 30.0° from the floor) to the bottom. The block then slides an additional 4.80 m along the floor before coming to a stop. Determine the coefficient of kinetic friction between block and floor.

Answer 1

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the block has mgh of PE when it starts, so at the bottom all that energy is kinetic.
Now, friction absorbs this energy, so

mu*mg*distance=mgh
solve for mu
Notice the distance is independent of mass. Neat experiment to show this.

Answer 2

distance down = 2.9 sin 30 = 1.45 meter

Ke at bottom = U at top = m g h = m*g*1.45 Joules

Work done by friction = that KE
mu m g * 4.8
so
m*g*1.45 = mu m g *4.8

mu = 1.45/4.8

note m g cancels

Answer 3

I am the one who nocks just put that in