A single conservative force acting on a particle within a system varies as F = (

Question

A single conservative force acting on a particle within a system varies as F = (Ax + Bx6)i N, where A and B are constants, F is in newtons, and x is in meters. (a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use any variable or symbol stated above as necessary.) U(x) = (b) Find the change in potential energy as the particle moves from x = 1.60 m to x = 3.60 m. (Use any variable or symbol stated above as necessary.) U = (c) Find the change in kinetic energy as the particle moves from x = 1.60 m to x = 3.60 m. (Use any variable or symbol stated above as necessary.) K =

Explanation / Answer

a) Apply, U(x) = -integrla F*dx

= -integral (-Ax + B*x^6)*dx

= A*x^2 - B*x^7/7

b) delta_U = U(x2) - U*x1)

= A*(3.6^2 - 1.6^2) - B*(3.6^7 - 1.6^7)/7

= 10.4*A - 1115.65*B

c) change in kinetic energy, delta_KE = -delta_U

= -10*A + 1115.65*B

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