Chapter 08, Problem 086 In the figure here, a small block is sent through point

Question

Chapter 08, Problem 086

In the figure here, a small block is sent through point A with a speed of 6.7 m/s. Its path is without friction until it reaches the section of length L = 13 m, where the coefficient of kinetic friction is 0.72. The indicated heights are h1 = 5.5 m and h2 = 2.0 m. What are the speeds of the block at (a) point B 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?

Explanation / Answer

a) Conserving energy

0.5mu^2 + mgh = 0.5mv^2

0.5*6.7^2 + 9.8*5.5 = 0.5*v^2

v = 12.4 m/s

b) Conserving energy

0.5mu^2 + mgh1 = mgh2 + 0.5mv'^2

0.5*6.7^2 + 9.8*5.5 = 9.8*2 + 0.5*v'^2

v' = 10.65 m/s

c) 0.5mv'^2 - umg*13 = left energy (if it crosses D)

Substituting we get negative energy which means it doesn't reach D

d) Let distance covered be P

0.5mv'^2 = umg*P

P = 8.04 m

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