Work, Energy and Power

Work done by gravity is the same along both paths.

Step 1: Gravity is a conservative force; its work depends only on the vertical displacement (height difference), not on the path. Step 2: Friction is a non-conservative force; its work depends on the length and nature of the path. Step 3: Since friction does negative work and is path-dependent, total mechanical energy is NOT conserved. Option A is wrong because friction is path-dependent. Option C is wrong because friction dissipates energy. Option D is the definition of a conservative force, which friction is NOT.

A: 0, B: v

Step 1: In an elastic collision between identical masses, velocities are exchanged. Step 2: Using the result for equal masses (mA = mB = m) with vBi = 0: vAf = vBi = 0 and vBf = vAi = v. Step 3: A comes to rest and B moves with A's initial velocity v. This is verified by checking both momentum (mv = mv ✓) and kinetic energy (½mv² = ½mv² ✓) conservation. Option A is the result of an inelastic collision. Option C means no collision happened. Option D violates energy conservation.

400 J

Step 1: By conservation of energy, all PE at the top converts to KE at the bottom. Step 2: PE at top = mgh = 2 × 10 × 20 = 400 J. Step 3: KE just before hitting ground = 400 J (since PE = 0 at ground level). Option A (200 J) uses g = 5 or h = 10 incorrectly. Option B (20 J) only uses mh. Option D (800 J) doubles the result.

0 J

Step 1: Work done = Fd cosθ, where θ is the angle between force and displacement. Step 2: Gravity acts vertically downward; displacement is horizontal. Step 3: θ = 90°, so cos 90° = 0. Step 4: W = mgh cos 90° = 0 J. The person does no work against gravity because there is no vertical displacement. Options A and B incorrectly assume vertical displacement. Option D is half of mgs which has no physical meaning here.