The two crates shown to the right are released from rest. Their masses are m_A =
ID: 1493556 • Letter: T
Question
The two crates shown to the right are released from rest. Their masses are m_A = 40.0 kg and m_B = 30.0 kg. The coefficient of kinetic friction between crate A and the inclined surface is mu_k = 0.150. What is their common speed when they have moved 40.0 cm. Use The Principle of Work and Energy for the system of the two crates to solve this problem. You need not "cut the cord" to solve this problem. (Suggestion: to calculate the work done by the weight force on the system, establish separate datums at the initial positions of crates A and B, as shown.)Explanation / Answer
Using work - energy theorem,
work done by gravity + work done by friction = change in KE
friction force, f = uk N = uk mA g cos@
mB g d + mA g d sin@ - uk mA g cos@ d = (mA + mB)v^2 /2 - 0
(30 x 9.8 x 0.40) + (40 x 9.8 x 0.40 x sin20) - (0.150 x 40 x 9.8 x cos20 x 0.40) = (30 + 40)v^2 /2
v = 2.06 m/s
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