Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on onlyr. That is, F(r) = F(r) `r. Show that a central force is a conservative force, by explicitly showing thatVx F = 0Q.n.4 Consider two particles of masses ml and m2. Let m1 be confined to move on a circle ofO plane, centered at x = y = 0. Let m2 be confined to move on a circle of radiusradius a in the z =b in the z = c plane, centered at x = y = 0. A light (massless) spring of spring constant k is attachedbetween the two particles.a) Find the Lagrangian for the system.Q.n.5 Oral Viva

Answered: Image /qna-images/answer/54b3d804-d2d1-4608-a5f1-dff97f14c311.jpg

Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on only r. That is, F(r) = F(r) r. Show that a central force is a conservative force, by explicitly showing that Vx F = 0

Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on only r. That is, F(r) = F(r) r. Show that a central force is a conservative force, by explicitly showing that Vx F = 0

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 52P

See similar textbooks

Related questions

Q: The lower part of the platform, whose vertical section is seen in the figure, is bent in the form of…

A: Given: The figure of an inclined platform with circular rail at the bottom is given. h is the height…

Q: A 50-N force is directed along the line drawn from the point whose x, y, z coordinates arc (8.2.3) m…

A: First find the unit vector joining the two point and multiple it to the force to get force vector.…

Q: B If the loop was initially at rest and floating in space and was free to move in any way…

Q: The two segments of the L-shaped bar are parallel to the x and z axes. The rope AB exerts a force of…

Q: Problem 4: A ball of mass M and radius R rolls smoothly from rest, at initial height h, down the…

Q: (c) Starting from the satellite on the Earth's surface at the equator, what is the minimum energy…

A: Given that Mass of satellite (m)= 220 kg Height of satellite (h)= 350 km Mass of earth(Me)= 5.97×…

Q: Verify that the Hamiltonian equation H(x, p, t) = T + V = p2/2m + (k/2) (x − v0t)2 leads to the same…

A: The Hamilton’s equations of motion are ∂H∂p=x˙, and ∂H∂x=-p˙ From Newton's second law p˙=mx¨

Q: a) Show that the torque on a planet orbiting the Sun due to the gravitational attraction of the Sun…

Q: Consider a particle moving at a constant speed in a straight line with no forces acting on it. For…

A: We'll answer the first question since the exact one was not specified.Please submit a new question…

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

Q: (c) To minimize the energy, differentiate the result to part (b) with respect to q, and set the…

Q: a cube of edge length a sits with one corner at the origin of an xyz coordinate system. A body…

A: (a) coordinates (0,0, 0) is very simple to be identified and clearly it is given as ??̂+ ??̂+ ??̂

Q: A ball is initially at rest at point 1. Aforce is applied to a wire, wrapped around the ball, which…

A: Here path is frictionless ,so no dissipation of energy takes place in form of friction .

Q: Problem 2: A fisherman has caught a fish on his pole, and to keep the pole steady he has to apply…

A: Consider the Figure shown below.

Q: Juan's teacher gives him three objects of equal volume and shape, but of different material, and…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

Q: In the Pirate Boat ride at the amusement park, riders swing back and forth in a pendulumlike “boat.”…

A: (a) The maximum height above the equilibrium point that is the lowest point is:

Q: Obtain the Thevenin equivalent as viewed from terminals: (a) a-b; and (b) c-d 6Ω 4Ω 120 V 3Ω 6 A (+

A: Given, a circuit To find thevenin equivalent across a-b & c-d using matrix form method

Q: A) Show that K.E can be expressed can be expressed a sum of K.E of motion of center of mass and K.E…

A: As per guidelines, first question (A) has been answered. With respect to centre of mass, position…

Q: A 8g mass is released from rest at C which has a height of 1.2m above the base of a loop-the-loop…

A: Given data: Mass m = 8g Height c from the base h =1.2 m Radius r=0.38m

Q: 1. A 150-N force acts in the direction defined by the direction angles ex-35° and ey=120°. Knowing…

Q: (b) As a spacecraft falls towards the Earth, it loses gravitational potential energy. What becomes…

A: 1. Hence, in the above question, Spacecraft loses its gravitational potential energy, when it coming…

Q: Particle of mass m slides without friction on a wedge of angle alpha and mass M that can move…

A: here we have to take the cartesian coordinate system with y=0 at the base of the wedge and x= 0 to…

Q: 13 B Consider the two vectors given in the figure, what is their DIFFERENCE in the unit vector…

A: From the figure we count the number of boxes to find out the unit vectors. The vector can be…

Q: (i) A particle P, of mass 2m, lies on a rough horizontal table. P is connected by a light…

Q: A solid sphere has a uniformly distributed mass of 1.0 * 104 kg and a radius of 1.0 m.What is the…

A: a) The expression for the magnitude of the force is,

Q: a) Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A box with its center of mass off-center as indicated by the dot is placed on an inclined plane. In…

A: For case A and B, the centre of mass is near the inclined plane. So, the block will slide

Q: A root locus of a system is sketched below (x indicates pole and o indicates zero) X pole Img O zero…

A: In this question we are given that a root locus of a system sketched as in the figure. We have to…

Q: (a) Show that if a particle describes a circular orbit under the influence of an attractive central…

A: Note: As per the guidelines, we can only answer three subparts of a question. Sorry for the…

Q: a) Consider a particle moving at a constant speed in a straight line with no forces acting on it.…

Q: etermine (a) the x, y, z components of the 200 N force in g. P1.3, (b) the angles Ox, Oy, and 0z…

A: components of a vector is obtained by resolution of vector

Q: (a) At what height above Earth’s surface is the energy required to lift a satellite to that height…

Q: n 3 of 11 Mickey, a daredevil mouse of mass M, is attempting to become the world's first "mouse…

Q: (a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an…

A: given, Vi = 5.96x104 m/s from conservation of energy, the initial total energy of the object at the…

Q: (a) Choose the plot that best describes the force versus x from x = 0 to x = 3.00 m. Fx (N) Fx (N)…

Q: Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on…

A: The vector differential operator of the spherical coordinate system is known as,…

Q: A particle moves in a force field described by the Yukowa potential V (r) = −k/r exp(−r/a) where k…

Q: Note: Make sure your calculator is in radian mode for this problem, and that you switch it back…

A: The x-component of impulse is given by, I21,x=∫titf F21,x dt

Q: 1. Write down the inertia tensor for a square plate of sidel and mass m for a coordinate system with…

A: We have a square plate of mass m and side l in the x-y plane. The z-axis passes through the center…

Q: g the 640-N cat burglar. (Assume the angle 0

Q: ehman Collec X The Division o Lehman Collec X Lehman Collec X Office of the R x A…

A: The expression for the gravitational potential energy is,

Q: E. An ant is on top of a flat table. Let the surface of the table be the x-y plane. Att= 0.0 s, the…

Q: If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity, its…

Q: The 55-kg package at Point A is rolling on a smooth ramp, where the ramp has two circular arcs AB…

A: (a) From the provided diagram, the vertical distance between point A to point B be:

Q: Given that A+2B-x,i+y,j and 2Ã-B- x,i+y,}, what is Ãz a. b.

Question

Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on only
r. That is, F(r) = F(r) `r. Show that a central force is a conservative force, by explicitly showing that
Vx F = 0
Q.n.4 Consider two particles of masses ml and m2. Let m1 be confined to move on a circle of
O plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius
radius a in the z =
b in the z = c plane, centered at x = y = 0. A light (massless) spring of spring constant k is attached
between the two particles.
a) Find the Lagrangian for the system.
Q.n.5 Oral Viva

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

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

97 PROBLEMS 2-45. Describe how to determine whe ther an equilibrium is stable or unstable when (dUdx),0. 2-46. Write the criteria for determining whether an equilibrium is stable or unstable when all derivatives up through order n, (d" U/ dx ") 0. 247. Consider a particle moving in the rCrion
A particle of mass m is projected upward with a velocity vo at an angle a to the horizontal in the uniform gravitational field of earth. Ignore air resistance and take the potential energy U at y=0 as 0. Using the cartesian coordinate system answer the following questions: a. find the Lagrangian in terms of x and y and identiy cyclic coordinates. b. find the conjugate momenta, identify them and discuss which are conserved and why c. using the lagrange's equations, find the x and y components of the velocity as the functions of time.
In a clamped frictionless pipe elbow (radius R) glides a sphere (weight W = mg) with zero initial velocity downwards from the top. %3D Determine the support reactions at the Clamping (wall connection) in dependence on the position o of the sphere. At which o the reactions take extreme values?
Observer A sees a moving charged particle collide with a stable stationary particle. The collision causes the stationary particle to break into two particles which move off afterward. To observers in other reference frames, O The same laws of physics hold, so the energies and momentuma are the same. O The beeakup of the particle may precede the collision. O The collision always precedes the breaking of the particle. O The stationary particle may not be stable.
let us imagine a scenario where we have two pendulums.. hehe. then we would have an elast1c collision when they both collide. look at the image and this is the scenario. lets say the left one is let go and it will hit the right one. we would have to assume m2=4m1 what will be the height of the left one after it hits the right one?
H.W: A frame ABC is supported in part by cable DBE that passes through a frictionless ring at B. Knowing that the tension in the cable is 385 N, determine (a)- the resultant ( R ) of the forces as a vector which exerted by the cables on the support at D and E, (b)- the angles between R and each of the coordinate axes. Answer: 280 mm 210 mm R= FRD + FRE =-(375 N)i + (455 N)j-(460 N)k E 0 = 120.1° = 52.5° 510 mm 400 mm 0. = 128.0° 600 mm 480 mm B.
u. IF AXB-0 prove that: RH à
A rocket in space (no friction or resistance to motion) can expel gases relative to itself at some high velocity V. Is V the upper limit to the rocket’s ultimate velocity?
A student fires a cannonball diagonally upwards with an initial speedv at an angle O as shown. Determine all unknowns and answer the following questions. Neglect drag and the initial height of the cannonball, Calculate the total flight time (t) and range (r) in each of the following cases. v [m/s] t[s] r [m] 20.0 35.0 25.0 35.0 30.0 35.0 35.0 35.0 35.0 55.0
(a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator, if for them? (b) What is their total energy (nearly the same as kinetic in this case) in GeV?
A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?
(a) Find the value of for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an observer measures it to be 25.0 m. (b) What is the of the spaceship relative to Earth?