A mysterious force has been discovered in nature that acts on all particles in the three-dimensional space. You determine that the force is always pointed away from a definite point in space, which we can call the force center. The magnitude of the force has the following functionality: F = Ae-br, where r is the distance from the force center to any other point.
Part (a)
Write an expression for the potential energy UD of a particle when it is at a distance D from the force center, assuming the potential energy to be zero when the particle is at in?nity.
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Part (b)
If D is measured in meters, then what must the units be for the proportionality constant A in order that the energy be in Joules?
Part (c)
If D is measured in meters, then what must the units be for the constant b in order that the energy be in Joules?
Part (d)
If the particle is a distance 0.11 m from the force center and the constants are A = 47 and b = 2, then what is the potential energy of that particle?