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Chapter 6: Problem 13
A crane lifts a 650 -kg beam vertically upward 23 m and then swings it eastward \(18 \mathrm{m}\). How much work does the crane do? Neglect friction, and assume the beam moves with constant speed.
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A typical bumblebee has mass 0.25 mg. It beats its wings 100 times per second, and the wings undergo an average displacement of about \(1.5 \mathrm{mm} .\) When the bee is hovering over a flower, the average force between wings and air must support the bee's weight. Estimate the average power the bee expends in hovering.
A force with magnitude \(F=a \sqrt{x}\) acts in the \(x\) -direction, where \(a=9.5 \mathrm{N} / \mathrm{m}^{1 / 2} .\) Calculate the work this force does as it acts on an object moving from (a) \(x=0\) to \(x=3.0 \mathrm{m} ;\) (b) \(3.0 \mathrm{m}\) to \(6.0 \mathrm{m}\) and (c) \(6.0 \mathrm{m}\) to \(9.0 \mathrm{m}\)
In midday sunshine, solar energy strikes Earth at the rate of about \(1 \mathrm{kW} / \mathrm{m}^{2} .\) How long would it take a perfectly efficient solar collector of \(15-\mathrm{m}^{2}\) area to collect \(40 \mathrm{kW}\). hof energy? (Note: This is roughly the energy content of a gallon of gasoline.)
(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?
A sprinter completes a 100 -m dash in 10.6 s, doing \(22.4 \mathrm{kJ}\) of work. What's her average power output?
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