Question

A single conservative force acts on a 5.00-kg particle within a system due to its interaction with the rest of the system. The equation Fx 5 2x 1 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x 5 1.00 m to x 5 5.00 m, calculate (a) the work done by this force on the particle, (b) the change in the potential energy of the system, and (c) the kinetic energy the particle has at x 5 5.00 m if its speed is 3.00 m/s at x 5 1.00 m.

Answer 1

Answer:

a) W =  40 J

b) -40 J

C) 62.5 J

Explanation:

Given data:

mass of particle is 5 kg

force equation is given as fx = 2x + 14

where fx force in newton

Fdx = (2x +  4)dx

integrated with respect to  x gives

$W = x^2 + 4x$

evaluated from 1.0 to 5.0 m:

$W = 5.0^2 + 4\times 5.0 - 1^2 + 4\times 1$

W =  40 J

b) - 40 J (force is conservative)

c) dU = -dK (change in potential = change in kinetic)

$Ki = 0.5\times m\times v^2$

$k initial = 0.5\times 5 \times (3)^2 = 22.5J$

Kf = Ki +  dK = 22.5J + 40J = 62.5