When the force F acting on a particle depends only on the particle's position coordinate x, and when the particle moves along the x-axis, then the work done by the force is the area under:
a) F versus x curve
b) F versus v curve (v is velocity)
c) F versus a curve (a is acceleration)
To determine which option represents the work done by the force, let's consider the definition and formula for work. Work, denoted by W, is the transfer of energy that occurs when a force acts on an object over a certain displacement. Mathematically, work is calculated as the dot product of the force and displacement vectors, given by:
W = F · d
where F represents the force vector and d represents the displacement vector.
In this case, when the force acting on the particle depends only on the position coordinate x, the work done by the force can be found by integrating the force with respect to the position over the entire range of motion. Since the particle moves along the x-axis, the displacement vector d can be represented as d = x_final - x_initial.
Now, let's consider the given options:
a) F versus x curve: Integrating the force with respect to x over the range of motion, i.e., from x_initial to x_final, represents the work done. Since the force depends only on x, this option is correct.
b) F versus v curve: Integrating the force with respect to v (velocity) is not applicable in this case because the force is not a function of velocity. Therefore, this option is not correct.
c) F versus a curve: Integrating the force with respect to a (acceleration) is also not applicable in this case because the force is not a function of acceleration. Therefore, this option is not correct.
In conclusion, the work done by the force is represented by the area under the F versus x curve (option a).