If the height of the object is lowered does the total energy of the object change?

Yes and no.





TE = PE + KE + WE; where TE is total energy, PE is potential, KE is kinetic, and WE is work energy done by or on the object.





When the object is lowered from a height h, the potential energy is reduced commensurately because PE(h) = mgh; where m is the object's mass and g = 9.81 m/sec^2 in SI units. To keep TE constant, which is what the conservation of energy says must happen, that potential energy loss must be compensated by an increase in kinetic energy, an increase in work, or both.





If the object is dropped in a frictionless environment, the only work done is WE = mgs; where s = H - h and H is the starting point for the fall and h is the current height above zero ground. In other words, the work, done by the gravitational force (W = mg) is just the force mg times the distance s fallen. This is the work function equation.





So in the frictionless environment, all the PE is converted into KE by the WE done on the object as it drops. And when the object is just about to hit ground zero, at h ~ 0, we have TE(0) = PE(0) + KE(0) = KE(0) because potential energy is almost zero as h ~ 0. That is, all the PE(h) = KE(0), which means all the potential energy at the start becomes kinetic energy. Thus, TE(h) = PE(h) = mgh = 1/2 mv^2 = KE(0) = TE(0) and the object retains its total energy throughout the fall up to just prior to impact with the ground level.





But if there is friction F (e.g., drag or sliding), the net force doing the work would be f = W - F and WE = fs = (mg - kN)s; where s is the distance the object is worked on by the two forces. I used F = kN; where k is the friction coefficient and N is the normal weight of the object. I could have used F = 1/2 rho Cd A v^2 which is the drag equation just as well.





Three things happen here with friction. PE goes down and KE goes up, same as in the frictionless environment. But with friction, some of the PE converts into heat and not into KE. It's the drag friction heat, for example, that makes the nose of a space shuttle glow white hot when penetrating the air. And guess what all that heat is doing...it's reducing the total energy of the shuttle.





That work generated heat is lost from the object. Recall TE(h = 0) = PE(0) + KE(0) + WE(0) when the object is lowered to just above ground level h ~ 0. Thus, just before impact with the ground, the object has a kinetic energy that is somewhat less than the potential energy it started with at h. Why? Because, with friction, not all the PE went into KE, as it did when we assumed no friction.





If you assume no friction in the descent, the object's TE does not change at all from when it was released or pushed down from h. In which case, the answer is no, the object's total energy does not change.





But if you assume friction, the object does not keep all that TE it started with. Some of it is vented, if you will, to the object's environment and that work energy is not associated with the object any more.





Thus, in the sense that some energy is lost due to friction, the total energy actually associated with the object just prior to impact is less than what it started with. In which case, yes, the total energy changes. In fact, because there is no such thing as a frictionless system in real life, the total energies at various waypoints in the system will in fact change.





So, my answer is yes for real life and no for frictionless make believe systems.If the height of the object is lowered does the total energy of the object change?
the energy of the 'system' changes, but not necessarially the energy of the object. Recall that energy is the 'potential to do work'.


The object itself has internal heat energy, maybe some chemical potential energy, maybe it is elastic and has some energy stored in compression. That remains the same no matter its position.


compare that to a 'system' where you are looking at an object suspended above some frame of reference (the ground?) by a shelf or rope or whatever other mechanism. at a given height it has some potential to do work. if it is lowered it first transfers potential energy into kinetic energy, then when it is brought to rest again that kinetic energy would be transfered into what ever braking system existed to stop its downward motion. so that system looses energy.


hope that addresses your question