A single conservative force F = (6.0x - 11)i N, where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 24 J at x = 0. (a) What is the maximum positive potential energy? At what (b) negative value and (c) positive value of x is the potential energy equal to zero?
Does the "i" in the force equation indicate that the force is always in the +y direction? Or is it a typo error?
If the force is in the y direction and the movement is along the x axis, the potential energy U does not change as a function of x, but it does depend upon y.
the i is the direction
To determine the maximum positive potential energy, we need to find the equilibrium position, where the force is zero.
Since the force F is given by F = (6.0x - 11)i N, we can set it equal to zero:
6.0x - 11 = 0
Solving for x, we find:
x = 11/6
Now, we can substitute this value of x into the potential energy equation U = 24 J to find the maximum positive potential energy:
U = 24 - (6.0 * (11/6))
U = 24 - 11
U = 13 J
So, the maximum positive potential energy is 13 J.
To find the negative value of x where the potential energy is zero, we set U equal to zero and solve for x:
0 = 24 - (6.0x - 11)
6.0x - 11 = 24
6.0x = 35
x = 35/6
Therefore, the potential energy is zero at x = 35/6 meters (or approximately 5.83 meters).
To find the positive value of x where the potential energy is zero, we set U equal to zero and solve for x:
0 = 24 - (6.0x - 11)
6.0x - 11 = 24
6.0x = 35
x = 35/6
Therefore, the potential energy is also zero at x = 35/6 meters (or approximately 5.83 meters).
So, the potential energy is equal to zero at negative and positive values of x, both at x = 35/6 meters (or approximately 5.83 meters).