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Chapter 6: Problem 31
A typical human diet is "2000 calories" per day, where the "calorie" describing food energy is actually 1 kilocalorie. Express 2000 kcal/day in watts.
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A meteorite plunges to Earth, embedding itself \(75 \mathrm{cm}\) in the ground. If it does 140 MJ of work in the process, what average force does the meteorite exert on the ground?
(a) Find the scalar product of the vectors \(a \hat{\imath}+b \hat{\jmath}\) and \(b \hat{\imath}-a \hat{\jmath}\) where \(a\) and \(b\) are arbitrary constants. (b) What's the angle between the two vectors?
By measuring oxygen uptake, sports physiologists have found that long-distance runners' power output is given approximately by \(P=m(b v-c),\) where \(m\) and \(v\) are the runner's mass and speed, and \(b\) and \(c\) are constants given by \(b=4.27 \mathrm{J} / \mathrm{kg} \cdot \mathrm{m}\) and \(c=1.83\) W/kg. Determine the work done by a 54 -kg runner who runs a 10 -km race at \(5.2 \mathrm{m} / \mathrm{s}\)
A 1400 -kg car ascends a mountain road at a steady \(60 \mathrm{km} / \mathrm{h},\) against a \(450-\mathrm{N}\) force of air resistance. If the engine supplies energy to the drive wheels at the rate of \(38 \mathrm{kW}\), what's the slope angle of the road?
A truck is moving northward at \(55 \mathrm{mi} / \mathrm{h}\). Later, it's moving eastward at the same speed. Has its kinetic energy changed? Has work been done on the truck? Has a force acted on the truck? Explain.
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