Prove that the force F = 2ex(- yzi + zj + yk) follows from a function potential energy and to determine it.
Q: Find the force corresponding to the potential energy U(x) = (Use the following as necessary: a, b,…
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Q: force in three dimensions is given by (a) F = FO(yx^- xy^) (b) F = F0(yx^ + xy^) where x^ and y^ are…
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A: Given : potential energy is U(x) = - a/x2 + b/x3
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Q: m, A particle of mass 2.00 × 10-10 kg is confined in a hollow cubical three-dimensional box, each…
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Q: Consider a force in R³ defined by F(x, y, z) = (6x²y2,4z³y + 2 y,0). Find the potential energy U(x,…
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Q: Find the force corresponding to the potential energy U(x) = (Use the following as necessary: a, b,…
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- Please show the work for the given question using the provided formula to arrive at the correct answer, thank you!this is done by the Lagrangian method. take a variation of kinetic energy expressions and same with potential energy and then combine it with virtual work to get the equation of motion. Variation calculus is needed. If you can get a differential equation representing motion by another method then it's cool.A particle, of mass m, is moving in one dimension under the influence of a conservative force with potential V (x). (a) If the potential is given by V (x) = x² – x*, (2) - find any equilibrium points and determine their stability. (b) The particle is started from the origin x = 0 with speed v, and moves under the influence of the potential V (x) defined in equation (2). How large does v need to be for the motion to be unbounded?
- The gravitational field of a spherical object at any distance from it points back to the center of the object. That is, in the field simulator it has arrows toward the center of the sphere. Put a test mass in this field and it will fall toward the center with increasing speed following the line of force. Locally, the field is the acceleration of gravity at that point. Now, how would you move a small mass so that you would not have to do work on it during the move? That work would be the change its energy. You would move it radially toward the center. You would move it radially away from the center. You would move it perpendicularly to the line of force, that is, move it in a local plane that is perpendicular to the radius at that point. There is no way to do this. Any displacement direction will take work.How would I be able to sketch the graph in problem 7.36?Write 5 logb u − 9 logb v as a single logarithm with a coefficient of 1. please show work
- m, A particle of mass 2.00 × 10-10 kg is confined in a hollow cubical three-dimensional box, each edge of which has a length, 2.00 × 10-10 and for which the potential energy function is zero inside, and infinite outside, the box. The total energy of the particle is 2.47 × 10-37 J. FindAs shown in the figure below, two masses m, = 4.70 kg and m, which has a mass 80.0% that of m,, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m, and m, start from rest, after they have each traveled a distance h = 1.60 m, use energy content to determine the following. (a) the speed (in m/s) v of the masses m/s (b) the magnitude (in N) of the tension T in the cordneed Answer only for (d)
- Consider a force in R3 defined by f(x,y,z)=(6*x*y^3, 9*x^2*y^2+2*y,0). Find the potential energy U(x,y,z) such that U(0,0,0)=0.a.) A particle with mass m is dropped with zero initial velocity a height h above the ground, under the action of the gravitational field (acceration constant g), such that it reaches the ground (z=0) with zero potential energy and velocity v>0. Determine h, in terms of the other quantities given. b.) Another particle moves with Simple Harmonic Motion with centre O.The particle has velocity 13ms–1 when it is 3m from O and 5ms–1 when it is 5m from O.(i) Find the period and amplitude of the motionI need the answer as soon as possible