Q.Distinguish between a conservative and a non-conservative force, giving one everyday example of each, and explain why the work done by a conservative force around any closed path is always zero.

A conservative force is one for which the work done on a body moving between two points depends only on those two points, never on the particular route taken between them. Gravity is the standard example: lifting a book from a table to a shelf and then lowering it back down to the table by any path at all -- straight up and down, or via a long, meandering route -- always involves exactly the same total work done by gravity over the whole round trip, namely zero, since the start and end heights coincide.

A non-conservative force is one for which this path-independence fails. Friction is the standard example: sliding a heavy trunk in a straight line from one corner of a room to another involves less work done against friction than sliding the very same trunk, between the very same two corners, along a long, winding path -- because friction opposes motion along whatever path is actually travelled, so the total distance covered, not just the net displacement between start and end points, determines how much work is done against it. …

State the path-independence definition of a conservative force with a gravity example and a friction counter-example, then show algebraically that …

• Giving an example (e.g. air resistance) but failing to explain why it is non-conservative, rather than just asserting it. …