# Lect_23 - ACT Heavy(real pulleys Lecture 23 Work and power...

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Lecture 23 Work and power for rotations. Examples. ACT: Heavy (real) pulleys Two blocks of masses m 1 and 2 (> 1 ) are connected through a string that goes through two different pulleys. Pulley 1 is made of plastic. Pulley 2 is made of iron. In both cases, 1 is initially at rest on the floor and 2 hangs at distance h from the floor. Both systems are released simultaneously. In which case does mass 2 hit the floor first? A. Case 1 B. Case 2 C. Same for both Case 1 (plastic) Case 2 (iron) 2 1 2 1 Case 1 (plastic) Case 2 (iron) 2 1 2 1 Rotational kinetic energy of the pulley: 22 2 11 24 rot KE I MR ω == 2 cylinder 1 2 IM R = In case 2, the rotation of the pulley absorbs a larger fraction of the energy available. 2 2 21 2 1 111 1 0 222 2 mgh mv  += + + +   v If string doesn’t slip on pulley: = () 2 12 1 M mmgh mm −= + + 2 1 ( ) 2 2 = ++

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Work done by a torque (for pure rotations) Work from θ 1 to 2 : τ d W z = 2 1 = If torque is constant, A force F acts on an object as it rotates from 1 to 2 . r Axis 1 2 = Work done along a small displacement: =⋅ G G dW dl = tan Fds ds = tan Frd Power done by a torque (for pure rotations) = Work done along a small displacement: dt P ω = = = Instantaneous power: t = = Average power: Important! These expressions are only true for pure
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Lect_23 - ACT Heavy(real pulleys Lecture 23 Work and power...

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