Final answer:
The work done to move an object from x = 1 meter to x = 4 meters in the presence of the force F(x)=3/x² along the x-axis is 2.25 Joules. This is calculated by evaluating the definite integral of the force over the distance.
Step-by-step explanation:
The work required to move an object from one point to another in the presence of a force field can be calculated by integrating the force over the distance traveled. In this case, the force F(x)=3/x² is a variable force acting along the x-axis, and we're interested in the work done to move an object from x = 1 meter to x = 4 meters. Using the work formula W = ∫ F(x) dx, where W is the work, F(x) is the force as a function of x, and dx represents an infinitesimal displacement along the x-axis, we can compute the work done.
The integral that represents the work done is:
W = ∫ F(x) dx = ∫ (3/x²) dx from x = 1 to x = 4
Calculating the integral gives us:
W = 3 [-1/x] from 1 to 4 = 3 [(-1/4) - (-1/1)] = 3 [(1 - 1/4)] = 3 [3/4] = 2.25 Joules.
The work done to move the object from x = 1 m to x = 4 m in the presence of a force given by F(x)=3/x² is therefore 2.25 Joules.