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
Videos
Textbook Question
Chapter 2, Problem 2.38P
The speed of a particle of mass m varies with the distance x as υ(x) = αx−n. Assume υ(x = 0) = 0 at t = 0. (a) Find the force F(x) responsible. (b) Determine x(t) and (c) F(t).
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A particle with unit mass moves under the influence of a force
F(t) = t â + e' ŷ + cos(t) 2.
If v (0) = 3 î + 2 ý + 2, find v(2).
Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin.
If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?
Problem 18: A particle of mass 0.61 kg begins at rest and is then subject to a force in the positive x direction that changes with time as given by the following function: F = mg[1-e-3.1t ], where g is the acceleration due to gravity.
Part (a) Determine the change in the velocity Δv of the particle between t = 0 and t = 2.3 sec.
Part (b) Determine the change in x-coordinate of the particle Δx between t = 0 and t = 2.3.
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
- A ball of mass m = 0.490 kg is dropped near the surface of the Earth.However, there exists an air resistance F = −βv, where β = 0.700 N · s/m. After a long time, the ballapproaches a speed v. What is this speed?arrow_forward: A body excutes S.H.M. of time period 8 sec. If its mass be 0.1 kg; its velocity 1 sec after it passes through its mean position be 4 m/s. Find its (i) total energy (ii) kinetic energy and (iii) potential energy.arrow_forwardA particle of mass 1.06 kg begins at rest and is then subject to a force in the positive x direction that changes with time as given by the following function: F = mg[1-e-2.1t ], where g is the acceleration due to gravity. Part (a) Determine the change in the velocity Δv of the particle between t = 0 and t = 2.4 sec. Part (b) Determine the change in x-coordinate of the particle Δx between t = 0 and t = 2.4.arrow_forward
- A particle of mass 1.15 kg is subject to a force that is always pointed towards the East but whose magnitude changes linearly with time t. The magnitude of the force is given as F = (6 N/s)t. Let the x-axis point towards the East. (a) Determine the change in the velocity Δv, in meters per second, of the particle between t = 0 and t = 1.2 sec. (b) Determine the change in x-coordinate Δx, in meters, of the particle between t = 0 and t = 1.2 if the initial velocity is 12.6 m/s, and points in the same direction as the force.arrow_forwardA particle of mass m is moving with speed v. If the mass of the particle triples, by what factor does its kinetic energy change?arrow_forwardu = 1.66 x 10-27 kg; v = 1.050x107 m/s. (in J) A uranium-238 nucleus undergoes a radioactive decay, The masses are approximately 238, 234 and 4 u, where u = the atomic mass unit. The U nucleus is initially at rest. Suppose the He nucleus has speed v. Then what is the kinetic energy of the Th nucleus? Parameters: A: 4.004x10-15 B: 5.006x10-15 C: 6.257x10-15 OC: 6.257x10-15 Submit Answer Tries 0/12 238 U Post Discussion → 234Th + 4He. D: 7.821x10-15 D: 7.821x10-15 OE: 9.776x10-15 F: 1.222x10-14 G: 1.528x10-14 H: 1.909×10-14 Send Feedbackarrow_forward
- An electron (mass = 9.11 × 10−31 kg) is accelerated along a straight line at 3.9 × 1014 ms−2.The electron has an initial speed of 3.2 × 106 ms−1 and travels a distance of 3.0 cm. Calculatethe electron’s: a) final speed.b) change in kinetic energy.arrow_forwardA constant force acts on a mass of 3kg for 1 minute and gives it a velocity of 2 m s−1 . Find the kinetic energy of the mass and the value of the force.arrow_forwardA particle with mass m=1 starts moving subject to a conservative force, with initial total energy E=4 Joules (=kgm^2s^−2). Find the potential energy of the particle at time t1, when it has velocity v(t1)=3(ms−1). U(t1)=arrow_forward
- If a particle is released from x = a, what is the minimum amount of kinetic energy required such that a particle never returns to the origin? Answer in terms of E0 (answer may contain e)arrow_forwardCalculate the kinetic energies (in J) of the following. (a) a 2,001.0 kg automobile moving at 130.0 km/h J (b) an 83 kg runner sprinting at 13 m/s J (c) a 9.1 ✕ 10−31 kg electron moving at 2.1 ✕ 107 m/s Jarrow_forwardA small spaceship with a mass of only 1.5 * 10^3 kg (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 10 kW laser beam, what speed will the ship attain in 1.0 day because of the momentum carried away by the beam?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Time Dilation - Einstein's Theory Of Relativity Explained!; Author: Science ABC;https://www.youtube.com/watch?v=yuD34tEpRFw;License: Standard YouTube License, CC-BY