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

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

the answer is f1 and d2 because if you put equal force on those two points the beam would balance trust me on this