Problem 1

Two small masses

m_1=2.0\,\mathrm{kg}

and

m_2=1.0\,\mathrm{kg}

are joined by a light inextensible string over an ideal pulley.

m_1

rests on a smooth plane inclined at

30^\circ

to horizontal and

m_2

hangs vertically. The system is released from rest; take

g=9.8\,\mathrm{m/s^2}

. (a) Find the acceleration and direction. (b) Find the tension and normal force on

m_1

. (c) Find the distance each mass travels in the first

2.0\,\mathrm{s}

, assuming the string stays taut.

problems.proof.stepOf

m_2g-T=m_2a,\quad T-m_1g\sin30^\circ=m_1a

problems.proof.analysis

Choose downward for $m_2$ and uphill for $m_1$ as positive. The inextensible string gives equal acceleration magnitudes in these chosen directions.