If the curl of the force is zero, then, the force is conservative. Determine if the force is CONSERVATIVE or NOT CONSERVATIVE: F = x²yz i – xyz² k Show the systematic/complete solution.
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Q: emonstrate whether or not this force is conservative.
A: For a force to be conservative its curl must be zero. ∇×F→=0 i^j^k^∂∂x∂∂y∂∂zFxFyFz=0
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- Can I see a random example of how you could set eq 6.4 and 6.5 equal to each other to find an expected speed. Thank youConsider the movement of a molecule of mass m beneath the impact of a force F = -Kr, where K could be a positive consistent and r is the position vector of the particle. (a) Demonstrate that the movement of the molecule lies in a plane. (b) Discover the position of the molecule as a work of time, expecting that at t = 0, x = a, y = 0, Vx = 0, Vy = V. (c) Appear that the circle is an ellipse. (d) Discover the period. (e) Does the movement of the molecule comply Kepler's laws of planetary motion? 76Determine whether the following is a conservative force. If it's conservative, suggest its potential.
- 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?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
- need help to figure this one outm, 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. Findprove this force are conserved F(x,y)=2a(x-y)i-a(2x-y)j Where a is constant
- Please answer within 90 minutes.The scalar triple product of three vectors is a • (b x c). Prove that the scalar triple product will not change when you cyclically permute the three vectors. (i.e., prove that a • (b x c) = b • (c x a) = c • (a x b) )Learning Goal: To understand the Equipartition Theorem and its implications for the mechanical motion of small objects. In statistical mechanics, thermal energy is the random motion of the microscopic world. The average kinetic or potential energy of each degree of freedom of the microscopic world therefore depends on the temperature. If heat is added, molecules increase their translational and rotational speeds, and the atoms constituting the molecules vibrate with larger amplitude about their equilibrium positions. It is a fact of nature that the energy of each degree of freedom is determined solely by the temperature. The Equipartition Theorem states this quantitatively: The average energy associated with each degree of freedom in a system at absolute temperature T is (1/2)k³T, where KB = : 1.38 × 10-2³ J/K is Boltzmann's constant. A "degree of freedom" corresponds to any dynamical variable that appears quadratically in the energy. For instance, (1/2)mv² is the kinetic energy of a…