Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2, Problem 2.12P
A particle is projected vertically upward in a constant gravitational field with an initial speed υ0. Show that if there is a retarding force proportional to the square of the instantaneous speed, the speed of the particle when it returns to the initial position is
where υt, is the terminal speed.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A space shuttle lands on a distant planet where the gravitational acceleration is 2.0 ( We do not know thelocal units of length and time , but they are consistent throughout the problem). The shuttle coasts along aleve, frictionless plane with a speed of 6.0. It then coasts up a frictionless ramp of height 5.0 and angle 0f 30°.After a brief ballistic flight, it lands a distance S from the ramp. Solve for S in local units of length. Assume theshuttle is small compared to the local length unit and that all atmospheric effects are negligible. Use x and y components.
At 45° latitude, the gravitational acceleration as a function of elevation z above sea level is given by g = a − bz, where a = 9.807 m/s2 and b = 3.32 × 10−6 s−2. Determine the height above sea level where the weight of an object will decrease by 1 percent.
How much work is required to lift a 900-kg satellite to
an altitude of 3· 106 m above the surface of the Earth?
The gravitational force is F = GMm/r², where M is
the mass of the Earth, m is the mass of the satellite,
and r is the distance between the satellite and the
Earth's center. The radius of the Earth is 6.4 · 10° m, its
mass is 6 · 1024 kg, and in these units the gravitational
constant, G, is 6.67 · 10-11.
Work =
(include units; for this problem assume all given constants
are accurate to many significant figures.)
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- How much work is required to lift a 800-kg satellite to an altitude of 3 · 106 m above the surface of the Earth? The gravitational force is F = GMm/r², where M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the satellite and the Earth's center. The radius of the Earth is 6.4 · 106 m, its mass is 6 · 10²4 kg, and in these units the gravitational constant, G, is 6.67. 10-¹¹. Work = (include help (units); for this problem assume all given constants are accurate to many significant figures.)arrow_forwardA balloon is rising from the earth's surface. The ascent velocity v, = 2 (m/s) is constant. The horizontal component of the speed of the balloon due to the wind is v, = 4y, where y is the height of the balloon from the ground. Find the drift distance in the horizontal direction when the balloon rises y = 40 (m). g = 10 (m/s²) A) 150 (m) В) 200 (m) С) 225 (m) D) 1600 (m) E) 960 (m)arrow_forwardA mass m is suspended from a massless spring of natural length 90 cm with the spring constant = 10 Nm and causes the spring to extend k by 9.1 cm. Assuming the gravitational field = 9.8 ms2, calculate the value of strength g the mass on the spring. Give your answer in SI units.arrow_forward
- One dimension. In the figure, two point particles are fixed on an x axis separated by distance d. Particle A has mass ma and particle B has mass 8.00 ma. A third particle C, of mass 63.0 ma, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and Cis zero? A В Number i Units *darrow_forwardHINT M. kg (a) Find the magnitude of the gravitational force (in N) between a planet with mass 6.50 x 1024 and its moon, with mass 2.55 x 10 kg, if the average distance between their centers is d= 2.90 x 108 m. %3D N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s? (c) What is the planet's acceleration (in m/s²) toward the moon? (Enter the magnitude.) m/s2arrow_forwardTwo forces act on a 2.55 kg object, the gravitational force and a second, constant force. The object starts from rest and in 1.20 s is displaced (4.05î – 3.30j) m. Write th second force in unit vector notation. (Enter your answer in kg • m/s?. Assume the gravitational force acts in the -j direction.)arrow_forward
- A force is specified by the vector F = (130i + 100j - 200k) N. Calculate the angles made by F with the positive x-, y-, and z-axes. Answers: 0x = Oy= 0 || 0₂ = D i iarrow_forwardConsider three masses, m¡ = 1 kg, m2 = 2 kg and m3 = 3 kg in the %3D shape of an isosceles right triangle with d= 0.2 m as shown below. Find the gravitational force on mị. Please express your answer as a vector in unit vector notation. y m1 45° m2 m3arrow_forwardA ski jumper starts from rest 45.0 m above the ground on a frictionless track and flies off the track at an angle of 45.0° above the horizontal and at a height of 19.5 m above the ground. Neglect air resistance. (a) What is her speed when she leaves the track? m/s (b) What is the maximum altitude she attains after leaving the track? m (c) Where does she land relative to the end of the track?arrow_forward
- Two celestial bodies, A and B, are located in space at coordinates (10, 12) and (-12, -15). Body A has a mass of 20 kg while body B has a mass of 40 kg. Determine the gravitational force exerted on body A by body B. A vector has a magnitude of 12 units and is directed at angle of 60°C from the positive x-axis. A scalar value of α -2 is multiplied. Determine the new magnitude and direction.arrow_forwardTwo forces act on a 3.25 kg object, the gravitational force and a second, constant force. The object starts from rest and in 1.20 s is displaced (5.60î – 3.30j) m. Write the second force in unit vector notation. (Enter your answer in kg · m/s2. Assume the gravitational force acts in the -j direction.) kg - m/s? F =arrow_forwardA ski jumper starts from rest 47.5 m above the ground on a frictionless track and flies off the track at an angle of 45.0° above the horizontal and at a height of 18.0 m above the ground. Neglect air resistance. (a) What is her speed when she leaves the track? m/s(b) What is the maximum altitude she attains after leaving the track? m(c) Where does she land relative to the end of the track? marrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Gravitational Force (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=pxp1Z91S5uQ;License: Standard YouTube License, CC-BY