Electromagnetic induction problems feel harder than they are because three quantities change simultaneously. The trick is to compute them in a fixed order every time.
Step one: identify the magnetic flux through the loop, Φ = BA cos θ. Determine which of B, A, or θ is changing.
Step two: apply Faraday's law to get the induced EMF, ε = −dΦ/dt. If a rod is sliding on rails at speed v through a field B, this simplifies to ε = BLv.
Step three: compute the induced current, I = ε/R. Get the sign right by Lenz's law: the induced current opposes the change in flux.
Step four: if the question asks about force, use F = BIL for the force on the current-carrying conductor. This force will oppose the motion that induced the current in the first place.
Energy questions on this topic almost always reduce to 'work done against the magnetic force equals electrical energy dissipated in the resistor'. Write that equation before computing anything.