Suppose force is applied on an object at an angle theta and the block moves for some distance along x axis
I understand that we take x component of force which is Force cos theta and multiply it with displacement vector. Why are we ignoring the y component here? Is it because the block moves along x direction?
What if force is applied at an angle theta to the ground and the block moves at an angle gamma to the ground. What will be the work done then?
Should it be F.d. cos (theta + gamma) ?
Best Answer
You are correct in answering most of your own questions. The Work done by the force on the object is equal to the component of the force that is tangent to the trajectory, i.e. along the path of motion. This turns out to be equal to dot(F, dx) where both inputs are vectors. This definition holds even for curved paths but you need to integrate along the path. This can be derived from Newton's laws, along with the definition of Kinetic Energy, by taking the dot product of both sides with v (velocity) and doing some change of variables. And yes, if both the force and the displacement make angles w.r.t the horizontal the correct angle to use is the sum or difference depending on which gives you the correct angle. I think in standard format you should have the difference between the two angles.