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Chapter 6: Q1Q (page 275)
Show that the units of andare indeed joules.
Both the terms and have the same unit, which is Joule
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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?
The escape speed from a very small asteroid is only 24 m/s. If you throw a rock away from the asteroid at a speed of 35 m/s, what will be its final speed?
You bring a boat toward the dock by pulling on a rope with a force of130 N through a distance of 6 M . (a) How much work do you do? (Include the appropriate sign.) (b) Then you slow the boat down by pushing against it with a force of 40 N, opposite to the boat’s movement of. How much work do you do? (Include the appropriate sign.) (c) What is the total amount of work that you do?
A protonand a deuteron (, “heavy” hydrogen) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3nucleus and a gamma ray (a high-energy photon, which has kinetic energy but zero rest energy):
This is one of the thermonuclear or fusion reactions that takes place inside a star such as our Sun.
The mass of the proton is 1.0073 u(unified atomic mass unit,), the mass of the deuteron is 2.0136 u, the mass of the helium-3nucleus is 3.0155 u, and the gamma ray is massless. Although in most problems you solve in this course it is adequate to use values of constants rounded to two or three significant figures, in this problem you must keep at least six significant figures throughout your calculation. Problems involving mass changes require many significant figures because the changes in mass are small compared to the total mass. (a) The strong interaction has a very short range and is essentially a contact interaction. For this fusion reaction to take place, the proton and deuteron have to come close enough together to touch. The approximate radius of a proton or neutron is about. What is the approximate initial total kinetic energy of the proton and deuteron required for the fusion reaction to proceed, in joules and electron volts ()? (b) Given the initial conditions found in part (a), what is the kinetic energy of theplus the energy of the gamma ray, in joules and in electron volts? (c) The net energy released is the kinetic energy of theplus the energy of the gamma ray found in part (b), minus the energy input that you calculated in part (a). What is the net energy release, in joules and in electron volts? Note that you do get back the energy investment made in part (a). (d) Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated? (For comparison, aroundare obtained from burning a mole of gasoline.) (e) Which of the following potential energy curvesin Figure 6.87 is a reasonable representation of the interaction in this fusion reaction? Why?
As we will study later, the average kinetic energy of a gas molecule is, whereis the “Boltzmann constant,”, andis the absolute or Kelvin temperature, measured from absolute zero (so that the freezing point of water is). The approximate temperature required for the fusion reaction to proceed is very high. This high temperature, required because of the electric repulsion barrier to the reaction, is the main reason why it has been so difficult to make progress toward thermonuclear power generation. Sufficiently high temperatures are found in the interior of the Sun, where fusion reactions take place.
Use energy conservation to find the approximate final speed of a basketball dropped from a height of m (roughly the height of a professional basketball player). Why don't you need to know the mass of the basketball?
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