Question

Find the force corresponding to the potential energy U(x)=−a/x+b/x2.

a) F(x) = -2a/x^3 + 2b/x^4
b) F(x) = -a/x^2 + 2b/x^3
c) F(x) = a/x^2 - b/x^3
d) F(x) = -a/x^2 - 2b/x^3

Answer 1

The correct force F(x) corresponding to the potential energy U(x) = -a/x + b/x² is found by taking the negative derivative, resulting in F(x) = -a/x² + 2b/x³.

Step-by-step explanation:

The force corresponding to the potential energy U(x) = -a/x + b/x2 can be found by taking the negative derivative of the potential energy with respect to position x. This relationship between force and potential energy can be represented by the equation F(x) = -dU/dx. Calculating this derivative step-by-step:

• First, taking the derivative of the first term -a/x with respect to x gives a/x2.
• Second, taking the derivative of the second term b/x2 with respect to x gives -2b/x3.
• Combining these results, and remembering to add the negative sign, we get F(x) = -a/x2 + 2b/x3.

Therefore, the correct answer is option b) F(x) = -a/x2 + 2b/x3.