A box slides from rest down a rough incline. Compared to an identical frictionless incline, what is true about the box's kinetic energy at the bottom?
AIt is the same — total energy is conserved in both cases
BIt is greater — friction converts potential energy more efficiently to kinetic energy
CIt is less — friction converts some mechanical energy to heat, reducing the final KE
DIt is less — friction increases the normal force, reducing the net work done by gravity
Friction does negative work (opposing motion), so W_total = W_gravity + W_friction, and W_friction < 0. By the work-energy theorem, ΔKE = W_total, so the final KE is less than it would be without friction. The missing mechanical energy is not destroyed — it becomes thermal energy in the surfaces. Total energy is conserved; only mechanical energy (KE + PE) is degraded. Option A confuses 'total energy conservation' with 'mechanical energy conservation' — a persistent error when non-conservative forces are present.
Question 2 True / False
A block is dragged from point A to point B along a rough surface via two different routes: one short and direct, one long and winding. Friction does more negative work along the longer route.
TTrue
FFalse
Answer: True
This is the defining property of non-conservative forces: the work they do depends on the path, not just the endpoints. W_friction = −μₖ·N·d, where d is the path length. A longer path means larger d, so friction does more negative work and removes more mechanical energy. This contrasts with conservative forces like gravity, where the work done depends only on the height difference regardless of path. Path-dependence is exactly what makes friction non-conservative.
Question 3 True / False
When friction acts on a sliding object, the total energy of the system (mechanical + thermal) decreases.
TTrue
FFalse
Answer: False
Total energy is always conserved. Friction converts mechanical energy into thermal energy — it does not destroy energy. The mechanical energy of the object decreases (W_friction < 0 means ΔE_mechanical < 0), but this is exactly offset by an equal increase in the thermal energy of the contacting surfaces. The statement 'friction dissipates energy' refers specifically to mechanical energy; the total energy budget is unchanged. This preview of thermodynamics — mechanical energy degraded to heat — is one of the conceptual payoffs of this topic.
Question 4 Short Answer
Why can't we define a potential energy function for friction, the way we define gravitational potential energy?
Think about your answer, then reveal below.
Model answer: Potential energy is defined for conservative forces because their work depends only on position (start and end points), not on path. Gravitational PE works because gravity does the same work between any two heights regardless of route — PE = mgh captures this path-independence. Friction's work depends on path length: drag an object in a complete circle and friction does negative work the entire time, even though you return to the starting position. There is no function of position whose change equals the work done by friction, so no potential energy can be defined for it.
The roundtrip test is the clearest diagnostic: a conservative force does zero net work on a closed loop (all PE is recovered). Friction always does negative work, accumulating energy loss on any loop. This path-dependence is precisely why PE cannot be defined and why mechanical energy is not conserved when friction is present.
Question 5 Multiple Choice
A block of mass 5 kg slides down a 3-meter rough ramp (30° incline, μₖ = 0.3), starting from rest. Which expression correctly gives the block's final kinetic energy?
AKE = mgh, using only gravity since friction is internal
BKE = mgh − μₖ·mg·cos(30°)·d, where d = 3 m is the ramp length
CKE = mgh + μₖ·mg·cos(30°)·d, because friction assists downward motion
DKE = 0, because friction converts all kinetic energy to heat on any slope
W_friction = −μₖ·N·d = −μₖ·mg·cos(30°)·(3 m), and W_gravity = mgh where h = 3·sin(30°) = 1.5 m. By the work-energy theorem: KE_f = W_gravity + W_friction = mgh − μₖ·mg·cos(30°)·d. Option A ignores friction (valid only on a frictionless surface). Option C has the wrong sign — friction opposes motion and removes energy. Option D would only hold if friction were enormous enough to prevent motion, which is not stated.