A 7 kg particle is in a potential given by U(x) = 3 x^4 - 1 x^2 - 4 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.

A particle moves in a potential given by U(x) = -7 x3 + 2.1 x (J).  Calculate the location of the stable equilibrium of this potential, in m. (Please answer to the fourth decimal place - i.e 14.3225)

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,

Consider two points in an electric field. The potential at point 1, V1, is 47 V. The potential at point 2, V2, is 174 V. An electron at rest at point 1 is accelerated by the electric field to point 2.  Part (a)  Express v2, the speed of the electron at point 2, in terms of ΔU, and the mass of the electron me.  v2 = √( - 2 ΔU/me )   Part (b)  Find the numerical value of v2 in m/s.  v2 =

Problem 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.1

What is the potential difference V(r) – V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)?

ANSWER 1 AND 5 ONLY