The only force acting on a particle is conservative force F. If the particle is at point A, the potential energy of the system associated with F and the particle is 39 J. If the particle moves from point A to point B, the work done on the particle by F is +25 J. What is the potential energy of the system with the particle at B?
To find the potential energy of the system with the particle at point B, we can use the relationship between work and potential energy.
The work done on the particle by a conservative force is equal to the negative change in potential energy. Mathematically, this can be represented as:
Work = -(Change in Potential Energy)
Given that the work done on the particle by the force is +25 J, we can rewrite the equation as:
25 J = -(Change in Potential Energy)
To find the change in potential energy, we need to multiply both sides of the equation by -1:
-25 J = Change in Potential Energy
Now, let's substitute the given potential energy of the system associated with the particle at point A into the equation. The potential energy at point A is 39 J, so we have:
-25 J = Potential Energy at B - 39 J
To solve for the potential energy at point B, we can add 39 J to both sides of the equation:
Potential Energy at B = -25 J + 39 J
Simplifying, we find:
Potential Energy at B = 14 J
Therefore, the potential energy of the system with the particle at point B is 14 J.