Question

A force parallel to the x-axis acts on a particle moving along the x-axis. This force is associated with potential energy u(x) given by u(x)=αx⁴, where α=0.630g/m⁴.

Option 1: αx²
Option 2: αx³
Option 3: αx⁴
Option 4: αx⁵

Answer 1

The potential energy function associated with the force is u(x) = αx⁴.

Step-by-step explanation:

The potential energy of a particle moving along the x-axis under the action of a force parallel to the x-axis is given by u(x) = αx⁴, where α = 0.630 g/m^4. The student is asked to determine the correct form of the potential energy function from the given options:

• Option 1: αx²
• Option 2: αx³
• Option 3: αx⁴
• Option 4: αx⁵

To determine the correct option, we compare the given potential energy function u(x) = αx⁴ with the options provided. It is clear that the correct option is Option 3: αx⁴ as it matches the given potential energy function exactly.