assignment3

# assignment3 - stable or not stable 3 A water droplet...

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Assignment 3 PHY 2030U Mechanics I Due October 14th, 2008 1. (2-43) A particle is under the inﬂuence of a force F = - kx + kx 3 2 , where k and α are constants and k is positive. Determine U ( x ), plot it, and discuss the motion in detail (see Example 2.13 for what to include in the discussion). What happens when E = (1 / 4) 2 ? Note: Don’t do this problem with Maple or something similar. Old school, by-hand only! 2. (2-42) A solid cube of uniform density and sides of b is in equilibrium on top of a cylinder of radius R (see ﬁgure below). The planes of four sides of the cube are parallel to the axis of the cylinder. The contact between cube and sphere is perfectly rough. Under what conditions is the equilibrium
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Unformatted text preview: stable or not stable? 3. A water droplet falling in the atmosphere is spherical. Assume that as the droplet passes through a cloud, it acquires mass at a rate proportional to kA , where k is a constant ( k > 0) and A is its cross-sectional area. Consider a droplet of initial radius r that enters a cloud with a velocity v . Assume no resistive force and show (a) that the radius increases linearly with the time, and (b) that if r is negligibly small the the speed increases linearly with the time within the cloud. 1...
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