Physics - Conservation of Mechanical Energy?

Question

Just a question that popped in my exam... Happened to be only I missed:

The sum of the potential and kinetic energies of a system is said to be conserved when

A) Only when the resultant force acting on the system is zero
B) Only when it moves in a closed cycle
C) Only when the work done by the resultant external force is zero
D) Always
E) None of the above

(or something like that)

I can't understand why A and C are wrong anyways.

Right answer is E by the way.

Answer 1

A) is not correct because of the word 'ONLY'. For example, consider the case of a body performing uniform circular motion. There is a resultant force acting on it called centripetal force which is not zero. But it does not do work. In this case inspite of the net resultant force, mechanical energy of the body is conserved.

C) This is wrong because the conditions to be satisfied for the law of conservation of mechanical energy to be valid are
( i ) the internal forces are conservative and
( ii ) the external forces do no work.
If the second condition is 'ONLY' satisfied and not the first one, meaning between different parts of the system in motion, if there is friction, the mechanical energy of the system is lost in overcoming friction in the form of heat. These frictional forces are internal.

Answer 2

E) None of the above

Thats the right answer

A) Only when the resultant force acting on the system is zero
is wrong , because if you are acclerating Mechanical energy is also conserved.

same to E.

Answer 3

I would say D
The energy is always conserved.
Pe+Ke+W+...=constant

A) Ft=0 means that a body moves with a constant velocity or is stationary. In this situation the energy is still conserved.

C) "work done by external force is zero" is perfectly fine as it has no influence on conservation of energy in the system.

Have fun

Answer 4

In all of these examples you would have a backward force (friction and drag) acting on the object to slow it down and decrease the mechanical energy (kinetic). Even though the first object is sliding on a frictionless surface it would still be affected by drag (air resistance) as it slides through the atmosphere. The only way to do this accurately is to have the object on a frictionless surface and in a vacuum.