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
Question
Chapter 2, Problem 2.31P
To determine
Show that in example 20, even if there was a component along x axis, the subsequent motion of the particle would be the same.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A particle of charge −q−q and mass m is placed at the center of a uniformaly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency f=1/2πVqQ/4πε0mR3
Consider a particle of electric charge e and mass m moving under the influence of a
constant horizontal electric field E and constant vertical gravitational field described by
acceleration due to gravity g. If the particle starts from rest, what will be its trajectory?
(a) parabolic
(b) elliptic
(c) straight line
(d) circular
Express the vector field W=(x^2-y^2)i +xzk in cylindrical coordinates at P(6,60degrees,-4).
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
Similar questions
- A charged particle moves along a straight line in a uniform electric field E with a speed v. If the motion and the electric field are both in the x direction, (a) show that the magnitude of the acceleration of the charge q is given by a=dvdt=qEm(1v2c2)3/2 (b) Discuss the significance of the dependence of the acceleration on the speed. (c) If the particle starts from rest at x = 0 at t = 0, find the speed of the particle and its position after a time t has elapsed. Comment on the limiting values of v and x as t .arrow_forwardA particle moves in the xy-plane under influence of the force field F = -kxi-ky 1. Prove that the path in which the particle moves is an ellipse.arrow_forwardEvaluate the line integral, where C is the given curve. Sc (x + yz)dx + 2x dy + xyz dz C consists of line segments from (1, 0, 1) to (2, 2, 1) and from (2, 2, 1) to (2, 4, 3). The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = is F(r) = Kr/1r|³ where K is a constant. Find the work done as the particle moves along a straight line from (5, 0, 0) to (5, 1, 5). Find the mass and center of mass of a wire in the shape of the helix x=t, y = 5cos(t), z = 5sin(t), 0 st ≤ 2π, if the density at any point is equal to the square of the distance from the origin. (mass) ) (center of mass)arrow_forward
- Consider an infinite long wire with a linear mass density p. If r denotes the distance from the wire, (a) find the gravitation field as a function of r. (b) find the gravitation potential as a function of r (you could leave a constant free parameter in the result). (c) For a particle of mass m released from rest at r=ro, what is the speed of the particle when reaching r=ro/2.arrow_forwardProblem 3.13 The gravitational force between two masses is F = −G (M₁ M2/r²) and the electrostatic = -k (Q1 Q2/r²). (a) Show that all massive objects attracted to force between two opposite charges is F the Earth will have the same acceleration independent of mass. (b) Show that two charged objects attracted to a point charge Q will not have the same acceleration unless both have the same charge to mass ratio.arrow_forwardGiven l, find the form of the potential U(r) such that the path of a particle subjected to this potential given by the spiral r(ϕ) = r0eαϕ, where r0 and α are constants. Discuss the physics of the system.arrow_forward
- There are N = 2400 electrons moving in one dimension and they meet at the origin of coordinates with a potential step of height Vo = 2,6eV. If each of the electrons have energy E = 3,1eV. Find the quantity of electrons that pass to the other region and the kinetic energy that they would carry.arrow_forwardVerify if the following vector fields are conservative: a) A1 = (2x / 1+x^2+y^2 , 2y / 1+x^2+y^2) b) A2 = (2xy − z^2 , 2yz + x^2 , y^2 − 2xz) In case they are conservative, find their respective potential fields.arrow_forwardPlease answer the ff and show the step by step solution including its units:arrow_forward
- We will do the following processes:a) First we take three point particles of mass (m1, m2, m3) from infinity and glue them to positions (x1, x2, x3) relative to some global inertial reference system.b) We now carry three positively charged particles qi, i ∈ (1, 2, 3) from infinity and glue them to positions (y1, y2, y3) relative to some global inertial reference system.Explain of these two processes if the external world gained or lost energy?Evaluate the energy gained or lost from the outside world. Is there conservation of energy in these processes?arrow_forwardHow would you solve this: In the search for the Higgs Boson, it was posited that the potnetial energy storedbetween two higgs particles is given by a 1 dimensional function of the distancebetween the two particles (x) as U(x) = c + ax2 − bx4 where a, b, c are constants.a) Find a function for the force as a function of position.b) what value of position (x) is the equilibrium position in terms of a and b.arrow_forwardProblem 2: A charged particle of mass m and positive charge q moves in uniform electric and magnetic fields E = Ey and B = B2. Suppose the particle starts at the origin with initial velocity vox. (a) Write down the (vector) equation of motion for the particle and resolve it into its three components. Show that the motion remains in the plane z = 0. (b) Prove that there is a unique value of vo, known as the drift speed var, for which the charge moves undeflected through the fields, and write an expression for var in terms of the given quantities. (c) Solve the equations of motion to find v(t), for arbitrary initial velocity vo in the x direction. It may be helpful to write your answer using dr. [Hint: try variable sub- stitution to simplify your differential equations. The drift speed seems important, so shift to a reference frame that moves at that speed.] (d) Integrate to find r(t), and plot the trajectory for several different and representative values of the ratio vo/vdr. For each…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning