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Chapter 6: Problem 57
Two unknown elementary particles pass through a detection chamber. If they have the same kinetic energy and their mass ratio is \(4: 1,\) what's the ratio of their speeds?
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After a tornado, a 0.50 -g drinking straw was found embedded \(4.5 \mathrm{cm}\) in a tree. Subsequent measurements showed that the tree exerted a stopping force of \(70 \mathrm{N}\) on the straw. What was the straw's speed?
Spider silk is a remarkable elastic material. A particular strand has spring constant \(70 \mathrm{mN} / \mathrm{m},\) and it stretches \(9.6 \mathrm{cm}\) when a fly hits it. How much work did the fly's impact do on the silk strand?
A sprinter completes a 100 -m dash in \(10.6 \mathrm{s}\), doing \(22.4 \mathrm{kJ}\) of work. What's her average power output?
A machine delivers power at a decreasing rate \(P=P_{0} t_{0}^{2} /\left(t+t_{0}\right)^{2}\) where \(P_{0}\) and \(t_{0}\) are constants. The machine starts at \(t=0\) and runs forever. Show that it nevertheless does only a finite amount of work, equal to \(P_{0} t_{0}\).
A force given by \(F=b / \sqrt{x}\) acts in the \(x\) -direction, where \(b\) is a constant with the units \(\mathrm{N} \cdot \mathrm{m}^{1 / 2} .\) Show that even though the force becomes arbitrarily large as \(x\) approaches zero, the work done in moving from \(x_{1}\) to \(x_{2}\) remains finite even as \(x_{1}\) approaches zero. Find an expression for that work in the limit \(x_{1} \rightarrow 0\).
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