A single conservative force acts on a 4.70-kg particle within a system due to it

Question

A single conservative force acts on a 4.70-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 = 1.06 m to x = 5.20 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 = 5.20 m if its speed is 3.00 m/s at x = 1.06 m
J

Explanation / Answer

a) x = 1.06 to x =5.2 m

Workdone, W = integral F*dx

= integral (2x + 4)*dx

= (x^2 + 4*x) (x = 1.06 to x =5.2 m)

= (5.2^2 + 4*5.2 - 1.06^2 - 4*1.06)

= 42.48 J

b) here total energy is conserved, because the work is done bu a conservative force.

kinetic energy increased.so, potentail energy is decreased.

change in the potential energy of the system = -42.48 J

c) Use, Work-energy theorem

Workdone = change in kinetic energy

W = 0.5*m*v2^2 - 0.5*m*v1^2

==> 0.5*m*v1^2 = 0.5*m*v2^2 - W

= 0.5*4.7*5.2^2 - 42.48

= 21.06 J

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