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Chapter 6: Q14CP (page 253)

In the given figure what kind of motion is represented by the situation with K + U = A? B? C?Think about the range of rin each situation, For example, Crepresents a circular orbit (constant r).

Short Answer

Expert verified

The potential energy is maximum and the kinetic energy is zero at A.

The kinetic energy is almost smaller than the potential energy at B.

The kinetic energy is half the potential energy at C.

Step by step solution

01

Definition of Kinetic energy(K)

The kinetic energy is the energy of an object or a system鈥檚 particles in motion. But it is affected by the environment outside of the object or system, such as air or height.

02

Determine range of r in each situation

At point C, if we consider the distance at C is half of r, therefore, the kinetic energy is half of the potential energy.

At point A, the potential energy reaches the maximum value where r is the maximum distance between the planet and star and as the potential energy is the maximum value, hence, the kinetic energy is almost zero and the planet begins to approach the star again at the closest point.

At point B, the system has both energies, kinetic energy and potential energy but the kinetic energy is almost smaller than the potential energy where K + U < 0.

Therefore, the kinetic energy is half the potential energy at C, the potential energy is maximum and the kinetic energy is zero at A, The kinetic energy is almost smaller than the potential energy at B.

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Most popular questions from this chapter

You stand on a spherical asteroid of uniform density whose mass is 2脳1016Kgand whose radius is 10Km. These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks.

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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,1.7脳10-27kg), 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 about1脳10-15m. 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 (1eV=1.6脳10-19J)? (b) Given the initial conditions found in part (a), what is the kinetic energy of theHe3plus the energy of the gamma ray, in joules and in electron volts? (c) The net energy released is the kinetic energy of theHe3plus 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 is32kbT, whereis the 鈥淏oltzmann constant,鈥�1.4脳10-23J/K, andis the absolute or Kelvin temperature, measured from absolute zero (so that the freezing point of water is273K). 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.
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