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HW1 - (5 pts c Find the translational and rotational energy...

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Physics 110, Problem set #1 Due April 7, 2010 1. (10 pts) Circular motion. a. A point mass circles around the Sun (mass 𝑀𝑀 ) at a fixed distance 𝑅𝑅 . Describe the motion in Cartesian coordinates ( 𝑥𝑥 ( 𝑡𝑡 ), 𝑦𝑦 ( 𝑡𝑡 )) , where the Sun is located at the origin. (5 pts) b. Explicitly show that the acceleration of the motion is in the direction of the Sun. (5 pts) 1. (15 pts) An iron bar starts to slip downwards without friction, as shown. Determine the force exerted by the wall as a function of h (initially, H h = ), until the top of the bar loses contact with the wall. 2. (15 pts) Rolling ball. a. Find the moment of inertia for a uniform, solid ball with mass M and radius R . (5 pts) b. The ball rolls down (without slipping) a slope with the angle of the incline θ , from an initial vertical height of
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Unformatted text preview: (5 pts) c. Find the translational and rotational energy of the ball. (5 pts) 3. (20 pts) Vector calculus a. Find the gravitational potential ) ( r Φ and gravitational field ) ( r g inside and outside of a solid sphere with uniform density ρ . (6 pts) b. In Cartesian coordinates, explicitly show that = × ∇ g . (7 pts) c. In Cartesian coordinates, explicitly demonstrate that the Poisson equation holds. (7 pts) 4. (20 pts) A ball slips down a smooth parabolic hill (described by the function 2 x y − = ) under gravity, as shown. a. Find the velocity v of the ball at a given location x . (8 pts) b. Find the force f exerted on the ball by the slope at a given location x . (12 pts) g l ) , ( g h...
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