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2008ex3sol - Summer 2008 third midterm two pages/sides...

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Summer 2008 – third midterm - two pages/sides Attempt in any order ALWAYS GIVE YOUR REASONING (1) (a) what is the momentary velocity (speed and direction) of the piece of rubber on the very front of a bicycle wheel when the bicycle is travelling at 10m/s? the bottom of the wheel is momentarily stationary, and the wheel rotates about it. the distance from the bottom of the wheel to the front is 2 times the distance to the hub, which is travelling at 10. so the answer is 10 2 the same answer can be obtained by adding the linear motion forward to the rotation around the axle hub. (b) a solid iron sphere of mass 1kg rolls down a 30 degree slope, for a distance of 2 meters. find its speed as it reaches the bottom. The moment of inertia of a sphere is I = 2 5 MR 2 height lost = 1 meter, so p.e. lost = 1(1g) =10 approx. this appears as linear + rotational kinetic energy. with M the total mass, mgh 10 = 1 2 mv 2 + 1 2 I ω 2 = 1 2 mv 2 + 1 2 2 5 mR 2 ω 2 = 7 10 mv 2 as v = mR with m = 1, v = 10 7 by coincidence (g~9.8) this is also nearly 14 (2) (a) can a ladder lean against a wall if there is a high coefficient of friction at the wall, but the floor itself is perfectly smooth? say why or why not.
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