Ch08-p067 - 67(a The assumption is that the slope of the bottom of the slide is horizontal like the ground A useful analogy is that of the pendulum

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(c) The assumption is no longer that the slope of the bottom of the slide is horizontal, but rather that the slope of the top of the slide is vertical (and 12 m to the left of the center of curvature). Returning to the pendulum analogy, this corresponds to releasing the pendulum from horizontal (at θ 1 = 90° measured from vertical) and taking a snapshot of its motion a few moments later when it is at angle 2 with speed v = 6.2 m/s. The difference in height between these two positions is (just as we would figure for the pendulum of length R ) Δ hR R R =− −− = 11 21 2 cos cos cos θθ bg where we have used the fact that cos 1 = 0. Thus, with Δ h = –4.0 m, we obtain 2 =70.5° which means the arc subtends an angle of | Δ | = 19.5° or 0.34 radians. Multiplying this by the radius gives a slide length of s' = 4.1 m. (d) We again find the magnitude f ' of the frictional force by using Eq. 8-31 (with W = 0): 0 1 2 2 =++ + ′′ ΔΔΔ KUE mv mgh
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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