Potential energy U = (k/2) x^3
F = -dU/dx
F = - d((K/2)x^3) / dx
= (-3k/2) x^2
so F = -(3k/2)x^2
so last option is the correct answer
Question 1 1 pts Given the following Potential Energy function with depends on the position ,...
using matlab
Question 1 130 pts Jmincon function to find the minimum value of the potential energy PE of following system: where P 50 N, k1 2 N/m, k2 5 N/m, k3- 4 N/m. The displacement of the masses A and B shall meet the requirement of, ki Use x1 search. = 1, x2 = 1 as the initial point for k3
Question 1 130 pts Jmincon function to find the minimum value of the potential energy PE of following...
A potential-energy function in two dimensions is given by U(x)=a(x2−y2), where x and y measure position in m and a is a positive constant with the units of J/m2J/m2. (a) Show that this function has an equilibrium at x=0, y=0. (b) Is the equilibrium stable against small displacements in the x-direction? What about the y-direction?
A particle has a potential energy given by the function PE = - 11x3 + 41x, where x is meters. Find the force on a particle at x = 4.0.
3. In Cartesian coordinates, a potential energy field U = 3x + 5 xe + 2 cos(az). a) What are the potential energy at position (0, 0, 0), (1, 1, 0) and (1, 1, 1)? (5 pts) b) Derive the force function F(x, y, z). Is this force conservative? (10 pts) c) What are the forces at position (0, 0, 0), (1, 1, 0) and (1, 1, 1)? (5 pts)
Given a potential energy function U(x), the corresponding force F is in the positive x direction if:a) u is positiveb) u is negativec) u is an increasing function of xd) u is an decreasing function of x
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Question 10 1 pts The graphs show potential energy diagrams for the same reaction at T-900. K R P 1) uncatalysed process; 2) catalysed reaction Uncatalyzed Reaction 400 300 reactants 200 100 products Reaction coordinate Uncatalysed reaction: Potential Energy (P.E.) vs reaction coordinate. Energy is measured from O to 400. kJ, and the reaction coordinate is associated with the evolution of the reaction. The PE of the reactants is 225 kJ. Then the energy grows to 400. kJ,...
8: Question 6. - 10.0 pts possible If the potential in a region is given by the function o 1. Ey = sin(z) V = 2 x – y2 – cos(2), O 2. Ey = –2y' what is the y-component of the electric field at the point P = (x', y', z')? 3. Ey = cos(z) O 4. Ey = 2 x' O 5. Ey = 2 0 6. Ey = y2 x2 7. Ey 4 8. Ey = 2y'...
How do I approach these questions?
Problem 9: The potential energy function for a conservative force Fc along the x-axis is U(x) = x3. (a) Use the potential energy function U(x) to calculate the force along the x-direction Fx. Answer: Fx = -3x2 (b) Calculate the work done by Fc when a particle moves from ti = 2 m to xf = 3. Answer: -19 J (c) This particle has a mass m= 2 kg. If the particle has a...
Question 28 1 pts What is the gravitational potential energy of a 1- kg block at rest on a table 1 m above the floor? 01 9.8 O 32 O 11.8) 00 Question 29 1 pts A particle is moved from point A to point B against a conservative force. Which statement is true about the work done? O cannot be recovered by moving it from B to A O does not depend on the path taken between A and...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown to the right. The function for the potential is: U(x)-k where γ 1.00 J.m2 and k-7.00 Jr. The particle has a mass of 3.00 kg. (a) Calculate the force on the particle as a function of position, F(x). (b) At which points, (A, B, C, D), must the particle be placed at rest such that it will stay at rest? Why must the particle...