The formulae to keep in mind here are:

W = Fcos(a)s where a is the angle between F and s, and s is the distance along the path of motion,

PE(gravity) = mgh,
PE(springs) = kx²/2,
KE = mv²/2.

All these problems can be solved with the application of these formulae (and sometimes the friction force formula). When mechanical energy is conserved, KE+PE=constant; when friction (or any other non-conservative force) is involved, the work done by that force must be included: KE+PE=constant+W_f.

1. Since there is no acceleration, there is no net force, so there is no net work on the object. Whomever is doing the pulling/pushing is doing work to overcome the friction.

3. mgh_final=0.5mv²_initial.

4. KE=PE-W_f.

7. Initial PE(gravity) equals final PE(spring); the system is frictionless, and the ore car is initially and "finally" (at the point of maximum spring compression) stationary.

11. Water rate times gh.