Final answer:
To find the work done for a force vector with a change in the x-axis, multiply the magnitude of the force with the magnitude of the displacement in the x-direction and cosine of the angle between the force and the displacement.
Step-by-step explanation:
The work done by a force is given by the formula W = F · d · cos θ, where W is the work done, F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and the displacement. In this question, if the force vector has a change in the x-axis, we can calculate the work done by multiplying the magnitude of the force with the magnitude of the displacement in the x-direction and cosine of the angle between the force and the displacement.
For example, if we have a force vector F = (3N)î + (4N)ĵ and a displacement from (0m, 0m) to (5m, 6m), we can calculate the work done as follows:
W = F · d · cos θ = (3N)(5m)cos 0° + (4N)(6m)cos 0° = 3N · 5m + 4N · 6m = 15Nm + 24Nm = 39Nm.
To find the work done by a force during a displacement along the x-axis, we need to look at the force vector that acts in the direction of displacement and the distance over which this force acts. If we consider a force vector F acting on an object that displaces it from xA to xB, the work done is calculated as the integral of the force with respect to displacement.
Specifically, for a spring force following Hooke's law, Fspring = -kx, where k is the spring constant and x is the displacement from the equilibrium position. The work done by this force as the object moves from xA to xB is the integral of Fspring dx, resulting in W = (1/2)kx2 from position xA to xB.