In the ramp below (see pic) the curved surfaces are frictionless, while the bott

Question

In the ramp below (see pic) the curved surfaces are frictionless, while the bottom has a coefficient of kinetic friction of mk=0.100 when a 2.0kg wooden block slides on it. The 2.0kg block is realeased as shown in the figure from an initial vertical height of 3.0m above the rough surface.

(a) Find the amount of work done by the kinetic friction, per metre of travel along the rough bottom.

(b) If the total length of the rough surface is 10.0m, how many times will the block move back and forth across the rough surface before coming to a complete stop?

Explanation / Answer

a) Work done by kinetic friction = f*10

==> W = mk*m*g*10 = 0.1*2*9.8*10 =19.6 J

work done per unit length = 19.6/10 = 1.96 J/m

b)conserving energy v = sqrt(2*9.8*3) = 7.67 m/s.............................................................

after 1st time through the rough surface v = sqrt(7.67^2 - 2*0.1*9.8*10) = 6.26 m/s......................

after 2nd time through the rough surface v = sqrt(6.26^2 - 2*0.1*9.8*10) = 4.43 m/s.....................................

after 3rd time through the rough surface v = sqrt(4.43^2 - 2*0.1*9.8*10) = 0.16 m/s....................................

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