PHY183-Lecture12pre-1

# PHY183-Lecture12pre- - Two Pulleys Ropes and pulleys can be combined to lift objects that are too heavy to lift otherwise Lets consider the case of

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1 February 1, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 12 Applications of Newton’s Laws Two Pulleys Ropes and pulleys can be combined to lift objects that are too heavy to lift otherwise Let’s consider the case of two pulleys One pulley is tied to the ceiling and the other is movable A mass m is hung from the movable pulley We pull down on the rope to lift the movable pulley We assume that the pulleys are massless and frictionless February 1, 2012 Physics for Scientists&Engineers 1 2 February 1, 2012 Physics for Scientists&Engineers 1 3 Two Pulleys (1) Mass m hung from a system of two pulleys February 1, 2012 Physics for Scientists&Engineers 1 4 Two Pulleys (2) First observation: tension in string is the same everywhere! Free-body diagram of block (in y direction): Free-body diagram of pulley B above block (also direction): F g T 3 = 0 T 3 = F g = mg 2 T 1 T 3 = 0 T 1 = 1 2 T 3 February 1, 2012 Physics for Scientists&Engineers 1 5 Two Pulleys (3) Combine these two equations: => Important result: If you use this pulley system, you only need to apply a force equal to 1/2 of the weight of the object. The pulley A only serves to redirect the force T 1 in this example: T 1 = 1 2 T 3 = 1 2 mg 2 T 1 T 2 = 0 T 2 = 2 T 1 February 1, 2012 Physics for Scientists&Engineers 1 6 Two Pulleys (4) Final remark: Combining all equations, we arrive at the conclusion: This means that the ceiling mount of the upper pulley carries the entire weight of the block (compare green circles) The entire force acting on the ceiling is exactly the same as the downward force on the rope, plus the weight of the block (see orange ovals) T 2 = 2 T 1 = 2( 1 2 T 3 ) = T 3 = F g

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2 February 1, 2012 Physics for Scientists&Engineers 1 7 Force Multiplier We can also use the same rope in loops and guide it over the same pulley multiple times In this example: 3 loops We have six force vectors pointing up, all with string tension T The object suspended from this pulley then can have a weight of 6 T In general for n loops: T = 1 2 n mg Applying Newton’s Laws Newton’s Laws allow to solve various kinds of problems involving force, mass, and acceleration Newton’s Second Law enables us to solve a wide range of calculations involving motion and acceleration Let’s consider an object of mass m located on a plane that is inclined by an angle θ
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## This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture12pre- - Two Pulleys Ropes and pulleys can be combined to lift objects that are too heavy to lift otherwise Lets consider the case of

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