When and for this v for this v performing the

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Unformatted text preview: hen . and , . For this v, . For this v, performing the differentiation, , as they should be. Extra Problem 1. 2. 3. In raising a mass m to a height h, the work done against gravity is W=mgh. If the total distance traveled is s (along the incline), then h = s sin(θ), giving W = mgs sin(θ). The work per meter per kg is then W/ms = g sin(θ). This is the function that is plotted in the figure. Since the angles are all pretty small, sin(θ) looks pretty linear. The difference between the walking curve (the lower curve) and the line g sin(θ) is the physiological inefficiency. a. You can eyeball the point where the curves are closest together, or notice that the minimum gap occurs when their slopes are equal. (Displace the straight line upward, keeping the slope the same, to convince yourself of this). b. A grade of about –2º or –2.5º gives the smallest inefficiency. c. At –2.5º, the gap is about 1.5 J/kg.m....
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This note was uploaded on 04/15/2010 for the course PHYSICS 16 taught by Professor N.darnton during the Spring '10 term at Smith.

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