Question

Q

Answer 1

First question, why is \(U_i=mgh_f\) instead of \(U_i = mgh_i\)?

Answer 2

that is the total energy of the system!! the energy of the system is constant if there were no other forces acting.
i.e. Kinetic Energy + Potential Energy = constant = total energy

now given that the pendulum starts from rest at height h_i,
K.E. = 0, total energy = P.E

Answer 3

But with the initial height hi, isn't the PE = \(mgh_i\)? Why is it \(mgh_f\)?

Answer 4

Initial PE = mg(l-lcosθi) = mgl (1-cosθi)
Final PE = mg(l-lcosθf)= mgl(1-cosθf)

PE loss = change in PE = mgl[(1-cosθf) - (1-cosθi)] = mgl(cosθi - cosθf) ??