A single conservative force acts on a 5.50-kg particle within a system due to it

Question

A single conservative force acts on a 5.50-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 = 0.90 m to x = 7.20 m, calculate the following.

(a) the work done by this force on the particle


(b) the change in the potential energy of the system


(c) the kinetic energy the particle has at x = 7.20 m if its speed is 3.00 m/s at x = 0.90 m

Explanation / Answer

a) Workdone = integral F*dx

= integral (2*x + 4)*dx

= x^2 + 4x

= (7.2^2 + 4*7.2) - (0.9^2 + 4*0.9)

= 76.23 J

b) change in potentail energy = -workdone

= -76.23 J

c) Apply conservation of energy

U1 + K1 = U2 + K2

K2 = K1 + (U1-U2)

= 0.5*m*v1^2 + (U1-U2)

= 0.5*5.5*3^2 + 76.23

= 101 J

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