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Chapter 7: Q24Q (page 170)
Bob and Jim decide to play tug-of-war on a frictionless (icy) surface. Jim is considerably stronger than Bob, but Bob weighs 160 lb whereas Jim weighs 145 lb. Who loses by crossing over the midline first? Explain.
Jimi crosses the midline first and loses.
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A 725-kg two-stage rocket is traveling at a speed of \({\bf{6}}{\bf{.60 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{m/s}}\) away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of \({\bf{2}}{\bf{.80 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{m/s}}\)relative to each other along the original line of motion.
(a) What is the speed and direction of each section (relative to Earth) after the explosion?
(b) How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]
A bullet of mass \(m{\bf{ = 0}}{\bf{.0010}}\;{\bf{kg}}\) embeds itself in a wooden block with mass \(M{\bf{ = 0}}{\bf{.999}}\;{\bf{kg}}\), which then compresses a spring \(\left( {k{\bf{ = 140}}\;{\bf{N/m}}} \right)\) by a distance \(x{\bf{ = 0}}{\bf{.050}}\;{\bf{m}}\) before coming to rest. The coefficient of kinetic friction between the block and table is \(\mu {\bf{ = 0}}{\bf{.50}}\).
(a) What is the initial velocity (assumed horizontal) of the bullet?
(b) What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block?
Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at\(15\;{\rm{km/s}}\). How much destructive energy could be released when it embeds itself in the Earth? (b) For comparison, a nuclear bomb could release about\(4.0 \times {10^{16}}\;{\rm{J}}\). How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth?
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