Q: Can kinetic and potential energy be used in projectile motion?
A: Absolute, the energy idea (Work-Energy theorem, Energy conservation) can be used in projectile motion, in which only Gravity force does work. However, if the problem asks for the direction of a vector (for example, velocity) in a projectile motion, we still need to use Dynamics (force/motion). Energy is Scalar, including no direction information!
Q: This question is asking for the work done by T1, T2, and Gravity. I understand How to get gravity, but I am confused about the distance in the work formula W=Fd. I understand that the distance is the tension force times cosine of the angle, but I don’t know how the angle is derived. The figure says 60 degrees for T2 and 45 degrees for T1, but the solution says that the angle for T1 is 150 degrees and the angle for T2 is 135.
A: I understand your confusion. Actually, W=Fd equation only applies to the case of force vector in parallel to displacement vector. The general equation of work is the Dot Product of Force and Displacement as seen in the picture.
For this problem, the displacement is Downward. The two tension forces directions are given in angles relative to the horizontal direction. We should find the angles theta of the tension forces relative to negative y direction (Downward) which are 150 degrees and 135 degrees according to Geometry, then use the equation of work W = F d cos(theta) to calculate the works done by the two tension forces.
