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264 CHAPTER 8 Conservation of Energy

45. How much energy is released by the annihilation of one
proton and one antiproton (both initially at rest)? Express
your answer in electron-volts.
46. How much energy is released by the annihilation of one elec-
tron and one antielectron (both initially at rest)? Express your
answer in electron-volts.
30
47. The mass of the Sun is 2 10 kg. The thermal energy in the
41
Sun is about 2 10 J. How much does the thermal energy
contribute to the mass of the Sun?
48. The masses of the proton, electron, and neutron are 1.672623
10 27 kg, 9.11 10 31 kg, and 1.674929 10 27 kg, respec-
tively. If a neutron decays into a proton and an electron, how
much energy is released (other than the energy of the mass of
the proton and electron)? Compare this extra energy with the
FIGURE 8.21 A whale breaching.
energy of the mass of the electron.
49. Express the mass energy of the electron in keV. Express the
measured from the water surface to the center of the whale. mass energy of the proton in MeV.
For a rough estimate of the energy requirements for such a 50. A typical household may use approximately 1000 kilowatt-hours
breach, we can treat the translational motion of the whale as of energy per month. What is the equivalent amount of rest mass?
that of a particle moving from the surface of the water upward 8
51. Combustion of one gallon of gasoline releases 1.3 10 J of
to a height of 3.0 m (for a more accurate calculation, we would
energy. How much mass is converted to energy? Compare this
have to take into account the buoyancy of the whale, which
with 2.8 kg, the mass of one gallon of gasoline.
assists it in getting out of the water, but let us ignore this).
52. A small silicon particle of diameter 0.20 micrometers has a
What is the initial speed of the whale when it emerges from 18
mass of 9.8 10 kg. What is the mass energy of such a
the water? What is the initial kinetic energy of a whale of 33
“nanoparticle” (in J)?
metric tons? Express the energy in kilocalories.
*53. In a high-speed collision between an electron and an antielec-
*43. The following table gives the rate of energy dissipation by a
tron, the two particles can annihilate and create a proton and
man engaged in diverse activities; the energies are given per
an antiproton. The reaction
kilogram of body mass:

e e S p p
RATE OF ENERGY DISSIPATION OF A MAN converts the mass energy and kinetic energy of the electron
(PER kg OF BODY MASS) and antielectron into the mass energy of the proton and the
antiproton. Assume that the electron and the antielectron
Standing 1.3 kcal/(kg . h) collide head-on with opposite velocities of equal magnitudes
Walking (5 km/h) 3.3 and that the proton and the antiproton are at rest immediately
after the reaction. Calculate the kinetic energy of the electron
Running (8 km/h) 8.2
required for this reaction; express your answer in electron-volts.
Running (16 km/h) 15.2
8.5 Power †
Suppose the man wants to travel a distance of 2.5 km in one-
half hour. He can walk this distance in exactly half an hour, or 54. For an automobile traveling at a steady speed of 65 km/h, the
run slow and then stand still until the half hour is up, or run friction of the air and the rolling friction of the ground on the
fast and then stand still until the half hour is up. What is the wheels provide a total external friction force of 500 N. What
energy per kg of body mass dissipated in each case? Which power must the engine supply to keep the automobile moving?
program uses the most energy? Which the least? At what rate does the friction force remove momentum from
the automobile?
8.4 Mass and Energy 55. In 1979, B. Allen flew a very lightweight propeller airplane
across the English Channel. His legs, pushing bicycle pedals,
44. The atomic bomb dropped on Hiroshima had an explosive supplied the power to turn the propeller. To keep the airplane
energy equivalent to that of 20000 tons of TNT, or 8.4 flying, he had to supply about 0.30 hp. How much energy did
13
10 J. How many kilograms of mass must have been converted he supply for the full flight lasting 2 h 49 min? Express your
into energy in this explosion? answer in kilocalories.

†
For help, see Online Concept Tutorial 10 at www.ww norton.com/physics