A single conservative force acts on a 4.90-kg particle within a system due to it

Question

A single conservative force acts on a 4.90-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 0.96 m to x = 4.90 m, calculate the following (a) the work done by this force on the particle J (b) the change in the potential energy of the system J (c) the kinetic energy the particle has at x = 4.90 m if its speed is 3.00 m/s at x = 0.96 m J

Explanation / Answer

a)work done=integral of f(x)*dx

so work done=(x^2+4*x) with x=0.96 to x=4.9

work done=38.85 J

b)

change in potential energy=-(work done)=-38.85 J

c)

if speed at x=4.9 is v,

then 0.5*4.9*(v^2-3^2)=33.85

v=4.7766 m/s

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