Chapter 08, Problem 086 in the ng re here, a small block i, sent through point A

Question

Chapter 08, Problem 086 in the ng re here, a small block i, sent through point A with a speed of 6 m/s. Its path is without friction until it reaches the section of length 1-12 m, where the coefficient of kinetic friction is 0.72. The indicated heights are h 5.4 m and 22.5m. What are the speeds of the block at (a) point 8 and (b) point C? (c) Does the block reach point D? (d) If so, what is its speed there; if not, how far through the section of friction does it travel? Unit (b) Number Unit Unit

Explanation / Answer

(A) Applying energy conservation,

PEi + KEi = PEf + KEf

m g h1 + 0 = 0 + m v^2 /2

v= sqrt(2 x 9.81 x 5.4) = 10.3 m/s

(B) m g h1 + 0 = m g h2 + m v^2 / 2

v = sqrt(2 x 9.81 x (5.4 - 2.5)) = 7.54 m/s

(C) on rough patch, a = - uk g = - 7.06 m/s^2

0^2 - 7.54^2 = 2(-7.06)(d)

d = 4.02 m

It does not reach D.

(d) d = 4.02 cm

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