Content check — College Physics (AP), Chapter 34: Frontiers of Physics

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Chapter 34: Frontiers of Physics

17 problems · 1 figure

Find the approximate mass of the luminous matter in the Milky Way galaxy, given it has approximately

10^{11}

stars of average mass 1.5 times that of our Sun.

Answer

3 \times 10^{41} kg

34-3 §34.1 source ↗

(a) Estimate the mass of the luminous matter in the known universe, given there are

10^{11}

galaxies, each containing

10^{11}

stars of average mass 1.5 times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mass? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then by

10^{9}

, since there are far more particles (such as photons and neutrinos) in space than in luminous matter.

Answer

(a) $3 \times 10^{52} kg$

(b) $2 \times 10^{79}$

34-5 §34.1 source ↗

On average, how far away are galaxies that are moving away from us at 2.0% of the speed of light?

Answer

0.30 Gly

34-7 §34.1 source ↗

(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than

0.9 c

Answer

(a) $2 . 0 \times 10^{5} km/s$

(b) $0.67 c$

34-9 §34.1 source ↗

Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass

1 . 5 \times 10^{11}

times that of the Sun (or

3 \times 10^{41} kg

), located 30,000 ly away.

Answer

2 . 7 \times 10^{5} m/s

34-11 §34.1 source ↗

Andromeda galaxy is the closest large galaxy and is visible to the naked eye. Estimate its brightness relative to the Sun, assuming it has luminosity

10^{12}

times that of the Sun and lies 2 Mly away.

Answer

6 \times 10^{- 11}

(an overestimate, since some of the light from Andromeda is blocked by gas and dust within that galaxy)

34-13 §34.1 source ↗

The average particle energy needed to observe unification of forces is estimated to be

10^{19} GeV

. (a) What is the rest mass in kilograms of a particle that has a rest mass of

10^{19} GeV/ c^{2}

? (b) How many times the mass of a hydrogen atom is this?

Answer

(a) $2 \times 10^{- 8} kg$

(b) $1 \times 10^{19}$

34-15 §34.1 source ↗

(a) What Hubble constant corresponds to an approximate age of the universe of

10^{10}

y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of

10^{10}

y. (b) Similarly, what Hubble constant corresponds to a universe approximately

2 \times 10^{10}

-y old?

Answer

(a) $30 km/s \cdot Mly$

(b) $15 km/s \cdot Mly$

34-17 §34.1 source ↗

The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, and so the neutron star spins rapidly. If the initial core radius is

5 . 0 \times 10^{5} km

and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the core’s angular velocity was originally 1 revolution per 30.0 days.

Answer

960 rev/s

34-19 §34.1 source ↗

Distances to the nearest stars (up to 500 ly away) can be measured by a technique called parallax, as shown in Figure 34.26. What are the angles

θ_{1}

and

θ_{2}

relative to the plane of the Earth’s orbit for a star 4.0 ly directly above the Sun?

The figure shows a conical shape with a star at the vertex, the Sun at the center of the circular base, and the Earth revolving around the Sun along the perimeter of the base. The star is 4 light years above the Earth-Sun plane. When the Earth is to the far left of the Sun, the angle between the line segment from the Earth to the Sun and the line segment from the Earth to the star is called theta one. When the Earth is in the diametrically opposite position (that is, the far right position) the angle between the same two lines is labeled theta two. — Figure 34.26 in the book ↗

Answer

89 . 999773º

(many digits are used to show the difference between

90º

)

34-22 §34.2 source ↗

What is the Schwarzschild radius of a black hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.

Answer

23.6 km

34-24 §34.2 source ↗

Supermassive black holes are thought to exist at the center of many galaxies.

(a) What is the radius of such an object if it has a mass of $10^{9}$ Suns?

(b) What is this radius in light years?

Answer

(a) $2 . 95 \times 10^{12} m$

(b) $3 . 12 \times 10^{- 4} ly$

34-26 §34.3 source ↗

The characteristic length of entities in Superstring theory is approximately $10^{- 35} m$ .

(a) Find the energy in GeV of a photon of this wavelength.

(b) Compare this with the average particle energy of $10^{19} GeV$ needed for unification of forces.

Answer

(a) $1 \times 10^{20}$

(b) 10 times greater

34-27 §34.4 source ↗

If the dark matter in the Milky Way were composed entirely of MACHOs (evidence shows it is not), approximately how many would there have to be? Assume the average mass of a MACHO is 1/1000 that of the Sun, and that dark matter has a mass 10 times that of the luminous Milky Way galaxy with its

10^{11}

stars of average mass 1.5 times the Sun’s mass.

Answer

1 . 5 \times 10^{15}

34-29 §34.4 source ↗

Assume the average density of the universe is 0.1 of the critical density needed for closure. What is the average number of protons per cubic meter, assuming the universe is composed mostly of hydrogen?

Answer

0.6 m^{- 3}

34-31 §34.6 source ↗

A section of superconducting wire carries a current of 100 A and requires 1.00 L of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost of cooling the wire must be less than the cost of energy lost to heat in the wire. Assume that the cost of liquid nitrogen is $0.30 per liter, and that electric energy costs $0.10 per kW·h. What is the resistance of a normal wire that costs as much in wasted electric energy as the cost of liquid nitrogen for the superconductor?

Answer

0.30 Ω

34-32 §34.6 source ↗

Critical Thinking Assume two galaxies are

2.00 \times 10^{2} Mly

apart. (a) How fast are they separating due to space expansion? (b) Now suppose a third galaxy is located

2.00 \times 10^{2} Mly

along a line that is a perpendicular bisector of the line segment between the first two galaxies. How fast is this galaxy separating from either of the other two galaxies? (c) Why would the third galaxy appear to be receding from both of the initially mentioned galaxies at the same rate? (d) How would the apparent motion be detected?

Answer

(a) $v =$ $H_{0} d =$ $(20 km/s) / Mly (2.00 \times 10^{2} Mly) =$ $4.00 \times 10^{3} km/s$

(b) $\begin{array}{l} d = \sqrt{{(1.00 \times 10^{2})}^{2} + {(2.00 \times 10^{2})}^{2}} Mly \\ = 2.24 \times 10^{2} Mly \\ v = (20 km/s) / Mly (2.24 \times 10^{2} Mly) = 4.48 \times 10^{3} km/s \end{array}$

(d) Light from the third galaxy would have a red shift when detected in either of the other galaxies.

End of the book.

Problems and answers are adapted from College Physics for AP® Courses 2e by Gregg Wolfe, Erika Gasper, John Stoke, Julie Kretchman, David Anderson and others, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/college-physics-ap-courses-2e/pages/1-connection-for-ap-r-courses. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.