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PHY183-Lecture10 - 1 Physics for Scientists& Physics for...

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Unformatted text preview: 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 February 1, 2011 Physics for Scientists&Engineers 1 1 Spring Semester 2011 Lecture 10 Applications of Newton’s Laws 2 Clicker Quiz Clicker Quiz Clicker Quiz Clicker Quiz s Choose the set of three coplanar vectors that sum to a net force of zero. Nope Nope Nope Nope February 1, 2011 Physics for Scientists&Engineers 1 2 Yep 3 Two Pulleys Two Pulleys Two Pulleys Two Pulleys s Ropes and pulleys can be combined to lift objects that are too heavy to lift otherwise s Let’s consider the case of two pulleys s One pulley is tied to the ceiling and the other is movable s A mass m is hung from the movable pulley s We pull down on the rope to lift the movable pulley s We assume that the pulleys are massless and frictionless February 1, 2011 Physics for Scientists&Engineers 1 3 4 Two Pulleys (1) Two Pulleys (1) Two Pulleys (1) Two Pulleys (1) s Mass m hung from a system of two pulleys February 1, 2011 Physics for Scientists&Engineers 1 4 5 Two Pulleys (2) Two Pulleys (2) Two Pulleys (2) Two Pulleys (2) s First observation: tension in string is the same everywhere! s Free-body diagram of block (in y direction): F g- T 3 = February 1, 2011 Physics for Scientists&Engineers 1 5 s Free-body diagram of pulley B above block (also y direction): T 3 = F g = mg 2 T 1- T 3 = T 1 = 1 2 T 3 6 Two Pulleys (3) Two Pulleys (3) Two Pulleys (3) Two Pulleys (3) s Combine these two equations: s => Important result: If you use this pulley system, you only need to apply a force equal to 1/2 of the eight of the object. T 1 = 1 2 T 3 = 1 2 mg February 1, 2011 Physics for Scientists&Engineers 1 6 weight of the object. s The pulley A only serves to redirect the force T 1 in this example: 2 T 1- T 2 = T 2 = 2 T 1 7 Two Pulleys (4) Two Pulleys (4) Two Pulleys (4) Two Pulleys (4) s Final remark: • Combining all equations, we arrive at the conclusion: • This means that the ceiling mount f the upper pulley carries the T 2 = 2 T 1 = 2( 1 2 T 3 ) = T 3 = F g February 1, 2011 Physics for Scientists&Engineers 1...
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