Final answer:
To find the work done by a force over a curve, integrate the force component in the direction of motion over the displacement from point A to point B.
Step-by-step explanation:
The work done by a force over a curve in the direction of increasing t can be found using the concept of integrating the force over the path taken by the object. When a force F is constant and the movement is in the direction of the force, work done is simply Fd cosθ where d is the displacement and θ is the angle between the force and the displacement.
However, if the force varies along the path, as in the case of a cubic or parabolic path, the work done is the integral of the force component in the direction of motion (F cos θ) over the displacement d.
In the specified problem, the force and path are given and we need to set up an integral to find the work done from point A to point B over the cubic path y = (0.25m-2)x3. Assuming a force field such as F = (5 N/m)yî + (10 N/m)xĵ, one must integrate the force in the direction of motion from point A to B.
The exact solution would depend on the specific details of the force vector and path defined by the student's problem, which needs further information for precise calculation. However, the methodology involves setting up the integral using the force components and the curve equation, and then computing the integral between the specified points A and B.
Your complete question is: Find the work done by F over the curve in the direction of increasing t. F = 2xyi + 2vj - 2vzk r(t) = ti + t^2j + tk, 0 leq t leq 1 Work =