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hw5 - Florida State University Department of Physics PHY...

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Florida State University Department of Physics PHY 5246 Assignment # 5 (Due Wednesday, 4th November, 2009) (1) (10 points) (a) A block sits on a frictionless plane inclined at an angle θ with the horizontal. The block is free to slide down the plane. Using the Lagrangian method with a suitably chosen constraint and Lagrange multiplier, obtain an expression for the acceleration of the block down the plane, and the normal reaction between the plane and the block. Use a set of axes in which the x -axis is horizontal and the y -axis is vertical. (b) Repeat the calculation of part (a), using axes that are parallel and perpendicular to the inclined plane. (2) (10 points) Fetter and Walecka 3.18. In answering the last part of this question, you will need to show explicitly whether or not the ladder leaves the floor. (3) (10 points) A block of mass m is held motionless on a frictionless plane of mass M and angle of inclination θ (see the figure). The plane rests on a frictionless horizontal surface. The block is released. Calculate the Lagrangian for the system, and obtain the equations of motion
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