(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider two masses of 3.3 kg and 7.4 kg

connected by a string passing over a pulley

having a moment of inertia 12 g · m2

about its axis of rotation, as in the ﬁgure below. The

string does not slip on the pulley, and the

system is released from rest. The radius of

the pulley is 0.35 m.

Find the linear speed of the masses after

the 7.4 kg mass descends through a distance

21 cm. Assume mechanical energy is conserved during the motion. The acceleration of

gravity is 9.8 m/s^2.

Answer in units of m/s

2. Relevant equations

delta PE = KE

KE = K(translational) + K(rotational)

3. The attempt at a solution

Found that change in potential energy should be equal to change in potential energy of the heavier mass (where PE is lost) subtracted by the change in potential energy of the lighter mass (where some PE is gained).

Therefore: 7.4*g*(21/100) - 3.3 * g * (21/100) = delta PE

I then set total change in KE to the delta PE. I determined rotational KE to be 1/2 I * omega^2

where I is given to me and omega is (v/r)^2 and r is given to me.

K translational = 1/2 * Mtotal * v^2. I factored out V^2, and set that equal to delta PE / rest of that mess

So in the end: v = sqrt ( delta PE / (6/r^2 + 1/2M)).

However, it wasn't the right answer :( so any ideas?

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# Conservation of energy and string pulley problem

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