Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 24, Problem 21E
Suppose you wanted to know the size of black holes with masses that are larger or smaller than the Sun. You could go through all the steps in Exercise 24.20, wrestling with a lot of large numbers with large exponents. You could be clever, however, and evaluate all the constants in the equation once and then simply vary the mass. You could even express the mass in terms of the Sun’s mass and make future calculations really easy. Show that the event horizon equation is equivalent to saying that the radius of the event horizon is equal to 3 km times the mass of the black hole in units of the Sun’s mass.
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Kirchoff's Laws. A circuit contains 3 known resistors, 2 known batteries, and 3 unknown currents as shown.
Assume the current flows through the circuit as shown (this is our initial guess, the actual currents may be
reverse). Use the sign convention that a potential drop is negative and a potential gain is positive.
E₂ = 8V
R₁₁ = 50
R₂ = 80
b
с
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11
www
12
13
E₁ = 6V
R3 = 20
a) Apply Kirchoff's Loop Rule around loop abefa in the clockwise direction starting at point a. (2 pt).
b) Apply Kirchoff's Loop Rule around loop bcdeb in the clockwise direction starting at point b. (2 pt).
c) Apply Kirchoff's Junction Rule at junction b (1 pt).
d) Solve the above 3 equations for the unknown currents I1, 12, and 13 and specify the direction of the current
around each loop. (5 pts)
I1 =
A
12 =
A
13 =
A
Direction of current around loop abef
Direction of current around loop bcde
(CW or CCW)
(CW or CCW)
No chatgpt pls will upvote
4.) The diagram shows the electric field lines of a positively charged conducting sphere of
radius R and charge Q.
A
B
Points A and B are located on the same field line.
A proton is placed at A and released from rest. The magnitude of the work done by the electric field in
moving the proton from A to B is 1.7×10-16 J. Point A is at a distance of 5.0×10-2m from the centre of
the sphere. Point B is at a distance of 1.0×10-1 m from the centre of the sphere.
(a) Explain why the electric potential decreases from A to B. [2]
(b) Draw, on the axes, the variation of electric potential V with distance r from the centre of the
sphere.
R
[2]
(c(i)) Calculate the electric potential difference between points A and B. [1]
(c(ii)) Determine the charge Q of the sphere. [2]
(d) The concept of potential is also used in the context of gravitational fields. Suggest why scientists
developed a common terminology to describe different types of fields. [1]
Chapter 24 Solutions
Astronomy
Ch. 24 - How does the equivalence principle lead us to...Ch. 24 - If general relativity offers the best description...Ch. 24 - Einstein’s general theory of relativity made or...Ch. 24 - If a black hole itself emits no radiation, what...Ch. 24 - What characteristics must a binary star have to be...Ch. 24 - A student becomes so excited by the whole idea of...Ch. 24 - What is an event horizon? Does our Sun have an...Ch. 24 - What is a gravitational wave and why was it so...Ch. 24 - What are some strong sources of gravitational...Ch. 24 - Suppose the amount of mass in a black hole...
Ch. 24 - Imagine that you have built a large room around...Ch. 24 - A monkey hanging from a tree branch sees a hunter...Ch. 24 - Why would we not expect to detect X-rays from a...Ch. 24 - Look elsewhere in this book for necessary data,...Ch. 24 - Which is likely to be more common in our Galaxy:...Ch. 24 - If the Sun could suddenly collapse to a black...Ch. 24 - Suppose the people in Figure 24.4 are in an...Ch. 24 - You arrange to meet a friend at 5:00 p.m. on...Ch. 24 - You are standing on a scale in an elevator when...Ch. 24 - Look up G, c, and the mass of the Sun in Appendix...Ch. 24 - Suppose you wanted to know the size of black holes...Ch. 24 - Use the result from Exercise 24.21 to calculate...Ch. 24 - Since the force of gravity a significant distance...
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