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 2.49P
To determine
Show that the period is proportional to
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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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- Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forwardModel the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forwardPlaskett'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…arrow_forward
- 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 Marrow_forwardStars 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.arrow_forwardIn the time of Johannes Kepler, it was believed that the orbit of Earth was circular, whereas the orbit of Mars was believed to be an oval (perhaps an ellipse), whose minor axis is 0.5% shorter than its major axis, so (a − b)/a ≈ 0.005. It was also known that the Sun is not at the center of this orbit; it is offset by about 10% of a. Kepler knew the geometry of ellipses very well, and recognized that this information made it quite likely that the orbit of Mars was actually an ellipse. Explain how he might have reached this conclusion (which was confirmed theoretically by Isaac Newton a half-century later).arrow_forward
- 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 = 170 km/s and the orbital period of each is 13.7 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 Need Help? Read It Master Itarrow_forwardYou are working at a summer internship for NASA, working to study exoplanets (planets we have detected around other stars). Calculate the orbital radius (distance of the planet to the star) of the newly detected planet Beta Sirius, if its' orbital period around its star is 5.51 x 107 s. You know from the data that the star has a mass of 2.21 x 1029 kg, and a radius of 2.70 x 106 and the planet has a mass of 3.00 x 1022 kg. Your Answer: Answerarrow_forwardOn October 15, 2001, a planet was discovered orbiting around the star HD68988. Its orbital distance was measured to be Part A 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. What is the mass of HD68988? For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Kepler's third law. Express your answer in kilograms. ΑΣφ ? M = kg Submit Request Answer Part B What is the mass of HD68988? Express your answer in terms of our sun's mass. M = Msun Submit Request Answerarrow_forward
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