Answer: A force parallel to the x-axis acts on a particle

Chapter 7, Problem 35E

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QUESTION:

Problem 35E

A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy U(x) given by U(x) = αx4, where α = 1.20 J/m4. What is the force (magnitude and direction) when the particles is at x = −0.0800 m?

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QUESTION:

Problem 35E

A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy U(x) given by U(x) = αx4, where α = 1.20 J/m4. What is the force (magnitude and direction) when the particles is at x = −0.0800 m?

ANSWER:

Solution 35E

Step 1:

The particle is moving in the x-axis and the potential is only a function of x. So, we don’t have to worry about the vectorial notation.

The potential energy is,

         .

We know that, force is the gradient of the potential. So,

       .

This is an attractive force which is clear from the minus sign.

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