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. Arianna is always the fastest in your team. While you were discussing with your friend, she was able to solve for the tension in the chain in terms of the mass m, the coefficient of kinetic friction and the angle at which we are pulling. This is all assuming the sled is moving at constant velocity. She found the following expression. cos θ + sin θ Before you start checking her math, you decide to make sure that she has the right units. Show that the units are good with Ariannas equation. ASSESS-check units! 10. You also check quickly what Arianna formula predicts when the angle 60. Does this limiting case make sense to you? ASSESS-check that 6-0 limit case make sense

11. You then work out below how she could have obtained this answer and you make sure that all the signs are right. (Show the steps!) SOLVE12. Once every member of the team has agreed that Ariannas first answer is correct, it quickly becomes obvious that it is possible to minimize the tension for a given mass (we want the minimum tension for a given mass because that means we can pull a larger mass for a given tension). The optimal angle for pulling will occur when cos θ + μκ sin θ is a maximum. At that point, the tension T will be a minimum because the relation is an inverse. At what angle is the function a maximum? [Hint: derivatives are useful for maximization problems. Also, two useful derivative formulas are: d(sin0)/d0 cos0, and d(cos0)/do--sin0.] SOLVE

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