The force F= (yzi + zxj + xyz)/xyz acts on the particle P(x,y,z) which moves in space. (a) Using the relation derived in Prob. 13.79, show that this force is a conservative force. (b) Determine the potential function associated with F.
Reference to Problem 13.79:
Prove that a force F(x,y,z) is conservative if, and only if, the following relations are satisfied:
Given data:
The force on a particle is: F
The potential function associated with force F is: V
The force act on the particle is given as,
Compared to the above equation with
Thus, we get,
(a)The force is conservative if it satisfied the expression given below,
Now, checking the expression,
The equation (1) is satisfied. Thus, the force F is a conservative force.
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