Consider a particle subject to the potential: V (x) : 1 + x² In other words: x' X' = y' dV dx x² -1 (x²+1)² Where: X(0) = C) ()- For what values of v does the particle reach x = 1?
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- A 8 kg particle is in a potential given by U(x) = 1 x^4 - 7 x^2 - 3 x + 8 (J). Calculate the acceleration of the particle when it is at x = 1 m, in m/s2. (Please answer to the fourth decimal place - i.e 14.3225)3. Consider the vector field F F(x, y, z) = sin yi + x cos yî + – sin zk. (a) Show this vector field is conservative. (b) For this vector field, find a potential function o which satisfies (0, 0,0) = 2020.3. Given the following scalar potentials (V), calculate the solution for the gradient of V (VV), and plot the vector arrow representation of this vector field over the given limits. (a) V = 15 + r cos o, for 0 < r < 10, and 0 < $ < 2n. (b) V = 100 + xy, for –10 < x < 10,
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