Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 2, Problem 2.48P
To determine
Show that the period is proportional to
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Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway
between them. This statement implies that the masses of the two stars are equal (see figure below). Assume
the orbital speed of each star is v| = 225 km/s and the orbital period of each is 11.6 days. Find the mass M
of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.)
M
XCM
M
Part 1 of 3 - Conceptualize
From the given data, it is difficult to estimate a reasonable answer to this problem without working through
the details and actually solving it. A reasonable guess might be that each star has a mass equal to or slightly
larger than our Sun because fourteen days is short compared to the periods of all the Sun's planets.
Part 2 of 3 - Categorize
The only force acting on each star is the central gravitational force of attraction which results in a centripetal
acceleration. When we solve Newton's second law, we can find the unknown mass in terms of the variables…
Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement
implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is V| = 200 km/s and the
orbital period of each is 11.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.)
| solar masses
M
XCM
M
Stars and black holes in a binary system orbit each other in circular orbits of radius r1 and r2 around their center of mass. Its mass is equal to 1.98x1030 kg, and its speed is 5.36 times faster than our Sun's. Furthermore, the visible star has an orbital period of 30 hours.(a) What is the apparent star's orbital radius, r1, in units of radii?In terms of MS, determine the black hole's mass m2. In the equation x3 = x(5a+5a)2, where an is the constant, x = 28a is a root.
Chapter 2 Solutions
Classical Dynamics of Particles and Systems
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - If a projectile is fired from the origin of the...Ch. 2 - A clown is juggling four balls simultaneously....Ch. 2 - A jet fighter pilot knows he is able to withstand...Ch. 2 -
In the blizzard of ’88, a rancher was forced to...Ch. 2 - Prob. 2.7PCh. 2 - A projectile is fired with a velocity 0 such that...Ch. 2 - Consider a projectile fired vertically in a...Ch. 2 - Prob. 2.11P
Ch. 2 - A particle is projected vertically upward in a...Ch. 2 -
A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 -
A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19PCh. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31PCh. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36PCh. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P
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