Answer :
1) It is a conservative force, yes.
2) At (5m, 5m), the potential energy is 20 J.
1) If the work that a force performs when moving an item depends only on the object's initial and final positions and not on the path travelled, the force is said to be conservative.
Let's verify if this condition is met for the force in this problem:
- For moving from (0 m, 0 m) to (5 m, 5 m), the work done is 20 J (A)
Then we can go from (0 m, 0 m) to (5 m, 5 m) through a different path:
- from (0 m, 0 m) to (5 m, 0 m) (work done: 25 J)
- from (5 m, 0 m) to (5 m, 5 m) (work done: -5 J)
Total work done in the second path: 25 J + (-5 J) = 20 J --> same as (A)
We can also go from (0 m, 0 m) to (5 m, 5 m) through a different path:
- from (0 m, 0 m) to (0 m, 5 m) (work done: 35 J)
- from (0 m, 5 m) to (5 m, 5 m) (work done: -15 J)
Total work done in the third path: 35 J + (-15 J) = 20 J --> same as (A)
So, the force is conservative, since the work done does not depend on the path taken.
2) For a conservative force, the change in potential energy of the object moved by the force is equal to the work done by the force in moving the object from A to B.
Here have:
Point A: (0m, 0m)
Point B: (5m, 5m)
In this problem, the potential energy at the origin (point A) is zero, so,
[tex]W = U_{b} - U_{a}[/tex]
Also we know that the work done is W = 20 J
So, we find
[tex]U_{b} = W + U_{a}\\=20 + 0\\= 20J[/tex]
Learn more about potential energy visit: brainly.com/question/10770261
#SPJ4
Correct Question:
A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from (0 m, 0 m) to (5 m, 0 m); 35 J from (0 m, 0 m) to (0 m, 5 m); -5 J from (5 m, 0 m) to (5 m, 5 m); -15 J from (0 m, 5 m) to (5 m, 5 m); and 20 J from (0 m, 0 m) to (5 m, 5 m).
Is this a conservative force?
If the zero of potential energy is at the origin, what is the potential energy at (5m, 5m)?