A particle of mass 2 kg is subjected to a two-dimensional conservative force given by, F x = -2 x + 2 y, Fy = 2 x - y 2 . (x, y in m and F in N). If the particle has kinetic energy of 8/3 J at point (2,3), find the speed (in m/s) of the particle when it reaches (1, 2).
Text Solution
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(2 m/s)
Sol. 
= F x 
+ F y 
. 
= – du
. 
= – du
F x dx + F y dy = – du
– du = (– 2x + 2y) dx + (2x – y 2 ) dy
= – 2x dx + 2(y dx + x dy) – y 2 dy
u (x, y) = x 2 – 2(xy) + 
+ C
U (2, 3) = 4 – 12 + 9 + C = 1 + C
+ 1 + C= (K.E) + [1 – 4 + 
+C]
Kinetic energy = 4 J
v 2 = 4
v = 2m\s
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