PHYSICS 8A-08 (03-16-10)

PHYSICS 8A-08 (03-16-10) - PHYSICS 8A Professor Joel Fajans...

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PHYSICS 8A Professor Joel Fajans 3/16/10 Lecture 17 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy, or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS I missed office hours yesterday. I apologize for the inconvenience. I previously announced that I wouldn’t be here at the end of the week. My plans have changed, and I will be here. LECTURE I left off last week discussing why it is better to carry a beam in the center than it is to carry a beam at the end. In the latter configuration, I have to push down—if I don’t the beam will tip and fall. Not only do I have to push down, I have to also push up with more force than if I were sensibly holding the beam in the center. I will run through the calculations of these forces today. What happens if I am holding the beam in the center? I assume all the mass is concentrated at the center. If I am holding this beam upright at the center, and the mass is concentrated at the center, then clearly the force at the arrow is ܨൌܯ݃ . Now suppose I am holding the beam some distance x from the end We want to figure out if this configuration is in static equilibrium. If it is then, the forces sum to zero, and the torques sum to zero. 0ൌܨ ௗ௢௪௡ െܨ ௨௣ ൅ܯ݃ ߬ൌ0ൌ0൅ݔܨ ௨௣ ܯ݃ܮ 2 If I want to figure out the torque, once again, I concentrate all the mass at the center. I calculate from the end, where I am applying ܨ ௨௣ . So I have zero from that term. The torque from the beam is equivalent to the total force times the moment arm to the center. Be careful about your signs! ܨ ௨௣ is trying to rotate counterclockwise, so the force from the mass acts in the opposite direction, and we get a negative sign for the last term. Solving our equations, we get ܨ ௨௣ ܯ݃ܮ 0ൌܨ ௗ௢௪௡ ܯ݃ܮ ൅ܯ݃ ܨ ௨௣ ܨ ௗ௢௪௡ ݔ
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PHYSICS 8A ASUC Lecture Notes Online: Approved by the UC Board of Regents 3/16/10 D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. 2 ܨ ௗ௢௪௡ ൌെܯ݃ ൬1െ ܮ Suppose I have one arm holding the beam up from the center and am pushing down with one arm. What force am I using the push down? 0, because there is no force acting up. We see this: ݔൌ ܮ 2 ܨ ௨௣ ܯ݃ܮ ݔ ൌܯ݃ ܨ ௗ௢௪௡ ൌܯ݃ ቌ1െ ܮ 2 ቍൌ0 Now suppose we are holding the beam closer to the edge: ݔൌ ܮ 10 ܨ ௨௣ ൌ5ܯ݃ Obviously, this is substantially greater than when I was holding the beam at the center. ܨ
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This note was uploaded on 04/29/2010 for the course PHYSICS 83840p3 taught by Professor Fajans during the Spring '10 term at Berkeley.

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PHYSICS 8A-08 (03-16-10) - PHYSICS 8A Professor Joel Fajans...

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