Calculate the acceleration of the particle when it is at x = 1 m, in m/s2.
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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)
potential of particle is given as
U(x) = x4-7x2-3x+8 J
The relation between force and potential is given as
F = -
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Solved in 2 steps
- (0,0,0) and the 5. The point o is the origin of the coordinate system, o = coordinates of b are b = (x,y, z). The electric potential at o is zero, V, = 0. Hence, the electric potential at b is V = – E · dr. You can take any path from o to b. (a) Here is one particular path from o to b. First move on a straight line from o to a = : (x,0,0), then from a to a' = (x, Y, 0), and finally from a' to b = (x, y, z). Make a plot of this path, indicating the coordinate system and the locations of a, a' and b. – SE • dr depends only on the y However, the line integral V coordinate of b = (x, y, z). Hence, in the following, we will focus on b = (0, y, 0) and take the straight path from o to b. (b) Compute E · dr for y d result, use this potential next.Determine whether the following is a conservative force. If it's conservative, suggest its potential.A particle moves in a force field described by the Yukowa potential V (r) = −k/r exp(−r/a) where k and a are positive. Show that if the orbit is nearly circular, the apsides will advance approximately by πρ/a per revolution, where ρ is the radius of the circular orbit.
- 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,Please explain An electrically charged particle is held fixed at the origin. Let V = 1/r be the potential energy of a second particle with unit electric charge located at (x, y, z), where r = sqrt(x^2 + y^2 + z^2). The force on this second particle is given by −∇V . Calculate the force on the particle when it is at (1, 2, −2). Show workingProblem Thirteen. A potential energy function is given by U(r)=U2 where o = 2.00 m r r and U, = 1.00 J. Find the magnitude of the force at r= 1.00 m. Give an answer in kN. 25.) (A) 280 (В) 106 (С) 420 (D) 470 (E) 530
- Homework Q.1A particle is trapped in a potential well described by U(x)= 1.9x2−b where U is in joules, x is in meters, and b = 2.6 J. Find the force on the particle when it's at x = 2.9 m.€1=15.0 4 |1=1.00 A MM Gelison R₂ = 200 [=100m E2= {3 = ₁ R₁ = 5,000 un 4.00 R = R₂ 1,00d 2.00 A @What is E₂ = 1 What is E3 = Wy what is the potential 0,5pts difference of brebtive to pont a (V₂a) ?