Chapter 7: Problem 16
Using momentum and force principles, explain why an air bag reduces injury in an automobile collision.
Chapter 7: Problem 16
Using momentum and force principles, explain why an air bag reduces injury in an automobile collision.
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Get started for freeAssume the nucleus of a radon atom, \({ }^{222} \mathrm{Rn}\), has a mass of \(3.68 \cdot 10^{-25} \mathrm{~kg} .\) This radioactive nucleus decays by emitting an alpha particle with an energy of \(8.79 \cdot 10^{-13} \mathrm{~J}\). The mass of an alpha particle is \(6.65 \cdot 10^{-27} \mathrm{~kg}\). Assuming that the radon nucleus was initially at rest, what is the velocity of the nucleus that remains after the decay?
In the movie Superman, Lois Lane falls from a building and is caught by the diving superhero. Assuming that Lois, with a mass of \(50.0 \mathrm{~kg}\), is falling at a terminal velocity of \(60.0 \mathrm{~m} / \mathrm{s}\), how much force does Superman exert on her if it takes \(0.100 \mathrm{~s}\) to slow her to a stop? If Lois can withstand a maximum acceleration of \(7 g^{\prime}\) s, what minimum time should it take Superman to stop her after he begins to slow her down?
A billiard ball of mass \(m=0.250 \mathrm{~kg}\) hits the cushion of a billiard table at an angle of \(\theta_{1}=60.0^{\circ}\) at a speed of \(v_{1}=27.0 \mathrm{~m} / \mathrm{s}\) It bounces off at an angle of \(\theta_{2}=71.0^{\circ}\) and a speed of \(v_{2}=10.0 \mathrm{~m} / \mathrm{s}\). a) What is the magnitude of the change in momentum of the billiard ball? b) In which direction does the change of momentum vector point?
Tennis champion Venus Williams is capable of serving a tennis ball at around 127 mph. a) Assuming that her racquet is in contact with the 57.0 -g ball for \(0.250 \mathrm{~s}\), what is the average force of the racquet on the ball? b) What average force would an opponent's racquet have to exert in order to return Williams's serve at a speed of \(50.0 \mathrm{mph}\), assuming that the opponent's racquet is also in contact with the ball for 0.250 s?
When you open the door to an air-conditioned room, you mix hot gas with cool gas. Saying that a gas is hot or cold actually refers to its average energy; that is, the hot gas molecules have a higher kinetic energy than the cold gas molecules. The difference in kinetic energy in the mixed gases decreases over time as a result of elastic collisions between the gas molecules, which redistribute the energy. Consider a two-dimensional collision between two nitrogen molecules \(\left(\mathrm{N}_{2},\right.\) molecular weight \(=28.0 \mathrm{~g} / \mathrm{mol}\) ). One molecule moves at \(30.0^{\circ}\) with respect to the horizontal with a velocity of \(672 \mathrm{~m} / \mathrm{s} .\) This molecule collides with a second molecule moving in the negative horizontal direction at \(246 \mathrm{~m} / \mathrm{s}\). What are the molecules' final velocities if the one that is initially more energetic moves in the vertical direction after the collision?
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