Physic Labs

Problem 1

Masses m1=2m_1=2 kg and m2=3m_2=3 kg hang from the ends of a light inextensible string passing over a fixed frictionless pulley of negligible radius. The system is released from rest and the string remains taut. Take g=10g=10 m/s2^2 and choose each mass's direction of motion as positive. (a) Determine the direction and acceleration of each mass. (b) Find the string tension. (c) Find their speed after moving s=0.80s=0.80 m from rest, and check it by energy conservation.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
v2=2as=2(2.0)(0.80)=3.2,v=1.79 m/sv^2=2as=2(2.0)(0.80)=3.2,\quad v=1.79\ \mathrm{m/s}
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The system starts from rest with constant acceleration, so the time-independent relation v2−v02=2asv^2-v_0^2=2as applies. The positive speed is common to both masses.

problems.proof.pitfall. Do not assign the same global sign to both masses and ignore the string constraint: their accelerations point oppositely but have equal magnitudes.