Answer: (a) The work done by this force on the particle is 42.71 J.
(b) The change in the potential energy of the system is -42.71 J.
(c) The kinetic energy the particle is 62.96 J.
Explanation:
(a) For the given situation, expression for work done is as follows.
W =
=
=
=
=
= 26.52 + 20.6 - 0.81 - 3.6
= 42.71 J
Hence, the work done by this force on the particle is 42.71 J.
(b) Expression for a conservative force is as follows.
F =
dU = -Fdx
=
= -42.71 J
Therefore, the change in the potential energy of the system is -42.71 J.
(c) According to the work energy theorem,
W =
= W
=
where, u = velocity of the mass at x = 0.9 m
u = 3.0 m/s, m = 4.50 kg
As,
=
= 62.96 J
Therefore, the kinetic energy the particle is 62.96 J.