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MT2 Review 2 - Physics 7A Midterm 2 Review November 5 2006...

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Unformatted text preview: Physics 7A Midterm 2 Review November 5, 2006 1. There is a point mass m a height h directly above a wide ring of inner radius a and outer radius b, as shown. The ring has total mass M. (a.) Find the gravitational force F(h) of the ring on the point. (b.) What—mathematically and physically—does this reduce to when h is much larger than both a and b? O m 2 2 h m fry 2. You have a yo-yo. How long Will it take to fall down and unwind under the force of gravity? (A yo—yo is effectively two cylinders of mass m1 and radius r1 connected at their centers by a spoke of mass m2 and radius T2, with r2 < n.) It starts at rest with a length 6 of very light string completely wrapped around its spoke, and falls to the end of the string without slipping as you hold the top of the string. Given: the rotational inertia of a cylinder is I = mr2 / 2. 3. A car, at rest at t = 0 s, accelerates at a constant rate in a circular track of radius 600 m. It reaches 90 km/ hr at t = 7 s. (a.) What are the radial and tangential accelerations of the car at t = 11 s? (b.) What are the angular velocity and acceleration at t = 11 s? (c.) The car has mass 1900 kg and coefiicient of friction 0.4 with the road. At what time does it fail to continue in the circle? 4. A uniform rope of mass per unit length A hangs from a hook so that its lower end just touches a table. It is then released from the hook and falls to the table. Find the force of the rope on the table as a function of m, g, and y, the distance from the top of the rope to the hook. Assume the rope is completely flexible and stops instantaneously when it hits the table. 5. As in the figure, a large spool of rope, radius R, stands on the ground as a person holds the end of the rope. (a.) The person first walks a distance L. (2.) How far does the spool’s center move? (22.) What length of rope unwinds from the spool? (b) Now the spool hits a step of height h < R. What force must the person apply (horizontally) to lift the spool over the step? " __,__;> ““112£14_ 1h 6. The potential energy of two atoms in a certain diatomic molecule can be written U(r) = —3+—b— 7.6 7.12 where 2" is the distance between the two atoms and a and b are positive constants. (a.) At what values of 2° is U at a minimum? A maximum? (b) At what values of r is U = 0? (0.) Plot U (2") (d.) Describe the motion of one atom with respect to the other when their total energy is E < 0, and when E > O. ...
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