Work-Energy Principle on Inclines

Steps:

• Distance along slope: $d = \frac{5.8}{\sin 20^\circ} \approx \frac{5.8}{0.342} \approx 17.0$ m.
• Work by pushing force: $W_p = 64 \times 17.0 = 1088$ J.
• Work against gravity: $W_g = mgh = 4.8 \times 9.8 \times 5.8 \approx 273$ J.
• Work against friction: $W_f = W_p - W_g \approx 1088 - 273 = 815$ J (≈810 J).

Why B is correct:

• By work-energy theorem, work against friction is total applied work minus gravitational potential energy change.

Why the others are wrong:

• A: Equals work against gravity only, ignoring applied force.
• C: Overestimates by using incorrect distance or force component.
• D: Approximates total pushing work without subtracting gravity.

Final answer: B