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Chapter 9: Problem 1
Roughly where is your center of mass when you're standing?
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An alpha particle ( \(^{4} \mathrm{He}\) ) strikes a stationary gold nucleus \(\left(^{197} \mathrm{Au}\right)\) head-on. What fraction of the alpha's kinetic energy is transferred to the gold? Assume a totally elastic collision.
A thin rod extends from \(x=0\) to \(x=L\). It carries a nonuniform mass per unit length \(\mu=M x^{a} / L^{1+a},\) where \(M\) is a constant with units of mass, and \(a\) is a non-negative dimensionless constant. Find expressions for (a) the rod's mass and (b) the location of its center of mass. (c) Are your results what you expect when \(a=0 ?\)
Physicians perform needle biopsies to sample tissue from internal organs. A spring-loaded gun shoots a hollow needle into the tissue; extracting the needle brings out the tissue core. A particular device uses 8.3 -mg needles that take 90 ms to stop in the tissue, which exerts a stopping force of \(41 \mathrm{mN}\). (a) Find the impulse imparted by the tissue. (b) How far into the tissue does the needle penetrate?
Two 140 -kg satellites collide at an altitude where \(g=8.7 \mathrm{m} / \mathrm{s}^{2}\) and the collision imparts an impulse of \(1.8 \times 10^{5} \mathrm{N}\) -s to each. If the collision lasts \(120 \mathrm{ms}\), compare the collisional impulse to that imparted by gravity. Your result should show why you can neglect the external force of gravity.
How is it possible to have a collision between objects that don't ever touch? Give an example of such a collision.
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