Show that f= 2xy+z3+x2j+3xz2 is a conservative force field ,find potential energy, find work done in moving object from (1,_2,1) to ( 3,1,4)

since the work done in closed path for above function is independent of the path so this is a conservative field

Explanation:

As we know that

now from above 3 equations we have

since the work done in closed path for above function is independent of the path

so this is a conservative field

Now work done in moving the object is given as

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.

you get 2.3=1.21*\frac{a}2 or 4.6=1.21a or a=3.802 (b)

explanation: