Work-energy theorem with friction

Steps:

• Calculate gravitational potential energy loss: mgh = (2.0 kg)(9.8 m/s²)(3.0 m) = 58.8 J.
• Calculate work done by friction: -f d = -(5.0 N)(7.0 m) = -35 J.
• Final kinetic energy: initial KE (0) + ΔPE + W_friction = 58.8 J - 35 J = 23.8 J.
• Speed: v = √(2KE/m) = √(2 × 23.8 J / 2.0 kg) = √23.8 ≈ 4.9 m/s.

Why A is correct:

• Matches the work-energy theorem: net work equals change in kinetic energy, yielding v ≈ 4.9 m/s.

Why the others are wrong:

• B ignores friction, giving √(2gh) ≈ 7.7 m/s (close but overestimate).
• C uses full slope distance for free fall, violating energy conservation.
• D assumes no friction and incorrect height, exceeding potential energy limit.

Final answer: A