Chapt. 8 Potential Energy and Mechanical Energy 87 HINT: A diagram might help. b) Find a formula for the force the groove exerts on the boll weevil as a function of θ . Take the radial inward direction as positive. Show all θ dependences EXPLICITLY . Simplify the formula as much as reasonably possible. The force could be called the groovy force. c) Find a 1st order di±erential equation for angular position θ with all θ ’s and θ derivatives shown EXPLICITLY . Don’t try to solve it, JUST ²nd it. Is the di±erential equation linear? Explain why it is linear or not. HINT: Start from the part (a) answer. d) An APPROXIMATE SOLUTION for the di±erential equation found in the part (c) answer is t = 1 r g/R ln b θ R ( g/R ) ω 20 + R ( g/R ) ω 20 θ 2 + 1 B , where θ is in RADIANS and ω0 = v0 /R . Note it turned out to be easier to get the slide-down time t as a function of θ than vice versa. Given that R = 2 . 0 m and ω0 = v
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