Physic Labs

Problem 1

Two masses m1m_1 and m2m_2 (m2>m1m_2>m_1) are joined by a light inextensible string over an ideal pulley; m1m_1 is on an incline of angle α\alpha with kinetic friction coefficient μ\mu, and m2m_2 hangs vertically. With constant gg, find the acceleration and string tension as m2m_2 descends. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.
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a=g[m2−m1(sin⁡α+μcos⁡α)]m1+m2a=\frac{g[m_2-m_1(\sin\alpha+\mu\cos\alpha)]}{m_1+m_2}
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Adding the two equations cancels the internal tension, leaving the net external force divided by total mass. This is consistent with the stated model and the chosen sign convention.