Problem 1

Two masses

m_1

and

m_2

(

m_2>m_1

) are joined by a light inextensible string over an ideal pulley;

m_1

is on an incline of angle

\alpha

with kinetic friction coefficient

\mu

, and

m_2

hangs vertically. With constant

g

, find the acceleration and string tension as

m_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.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

m_2g-T=m_2a,\quad T-m_1g\sin\alpha-f_k=m_1a

problems.proof.analysis

Take downward for $m_2$ and up the incline for $m_1$ as positive; the inextensible string imposes equal acceleration magnitudes. This is consistent with the stated model and the chosen sign convention.

problems.proof.pitfall. Do not assign the same geometric positive direction to both bodies; the string constrains acceleration magnitudes.