Final answer:
The student's question is about finding the total work done by a variable force F(x) over a displacement of 10 m by integrating the force function with respect to position.
Step-by-step explanation:
The student is asking for the amount of work done by a force F(x) that varies with position x, over a distance from x = 0 to x = 10 m. This is a Physics problem that involves calculating work done by a variable force, which is an integral of the force over the distance. The force in question is F(x) = (10 N)sin[(0.1 m⁻¹)x]. To find the total work done, we need to integrate F(x) with respect to x from 0 to 10 m.
To solve for the work done, the integral of F(x) dx from 0 to 10 m is calculated using the equation W = ∫ F(x) dx, which represents the work done by the force over the displacement. Given that the force is a function of the sine of a multiple of x, integrating F(x) will involve a sine integral that will yield the result of the work done.