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Chapter 6: Q16 P (page 276)
One mole of helium atoms has a mass of grams. If a helium atom in a balloon has a kinetic energy of, what is the speed of the helium atom? (The speed is much lower than the speed of light.)?
The speed of helium atom is,.
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Figure 6.77 is a graph of the energy of a system of a planet interacting with a star. The gravitational potential energy is shown as the thick curve, and plotted along the vertical axis are various values of
Suppose that of the system is A. Which of the following statements are true? (a) The potential energy of the system decreases as the planet moves from to. (b) When the separation between the two bodies is , the kinetic energy of the system is . (c) The system is a bound system; the planet can never escape. (d) The planet will escape. (e) When the separation between the two bodies is, the kinetic energy of the system is (B 鈭� C). (f) The kinetic energy of the system is greater when the distance between the star and planet is than when the distance between the two bodies is.
Suppose instead that of the system is B. Which of the following statements are true? (a) When the separation between the planet and star is, the kinetic energy of the system is zero. (b) The planet and star cannot get farther apart than. (c) This is not a bound system; the planet can escape. (d) When the separation between the planet and star is, the potential energy of the system is zero.
It is not very difficult to accelerate an electron to a speed that is of the speed of light, because the electron has such a very small mass. What is the ratio of the kinetic energy K to the rest energy in this case? In the definition of what we mean by kinetic energy K, , you must use the full relativistic expression for E, because v/c is not small compared to 1.
In the preceding example, at the final speed, 0.9997 c, what was the particle energy as a multiple of the rest energy ? (That is, if it was twice , write .) What was the kinetic energy as a multiple of? Was the kinetic energy large or small compared to the rest energy? At low speeds, is the kinetic energy large or small compared to the rest energy?
Turn the argument around. If the object falls to the Earth starting from rest a great distance away, what is the speed with which it will hit the upper atmosphere? (Actually, a comet or asteroid coming from a long distance away might well have an even larger speed, due to its interaction with the sun.) Small objects vaporize as they plunge through the atmosphere, but a very large object can penetrate and hit the ground at very high speed. Such a massive impact is thought to have killed off the dinosaurs.
The point of this question is to compare rest energy and kinetic energy at high speeds. An alpha particle (a helium nucleus) is moving at a speed of times the speed of light. Its mass is (a) what is its rest energy? (b) Is it okay to calculate its kinetic energy using the expression?(c) What is its kinetic energy? (d) Which is true? A. the kinetic energy is approximately equal to the rest energy. B. The kinetic energy is much bigger than the rest energy. C. The kinetic energy is much smaller than the rest energy.
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