In the figure here, a small block is sent through point A with a speed of 6.2 m/

Question

In the figure here, a small block is sent through point A with a speed of 6.2 m/s. Its path is without friction until it reaches the section of length L = 12 m, where the coefficient of kinetic friction is 0.73. The indicated heights are h_1 = 5.6 m and h_2 = 2.5 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? (a) Number Unit (b) Number Unit (c) (d) Number Unit

Explanation / Answer

a) Use (K + U)A = KB

So 1/2*m*vB^2 = 1/2*m*vA^2 +m*g*h1

so vB = sqrt(vA^2 +2*g*h1) = sqrt(6.2^2 + 2*9.8*5.6) = 12.18 m/s

b) KB = (K + U)C

So KC = KB - UC...1/2*m*vC^2 = 1/2*m*vB^2 - m*g*h2

So vC = sqrt(vB^2 -2*g*h2) = sqrt(12.18^2 - 2*9.8*2.5) = 9.97 m/s

c) If the work done by friction is > KC then the block does not reach D

d) W = µ*m*g*L = 0.73*g*L = 0.70*9.8*12 = 85.94 J/kg

KC = 1/2*v^2 = 1/2*9.97^2 = 49.7 J/kg so the block does not reach D



so vD = sqrt(vC^2 - 2*µ*g*L) = sqrt(9.97^2 -2*0.73*9.8*12) = 5.08m/s

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