Which scenario requires the greatest amount of mechanical work?

Which scenario requires the greatest amount of mechanical work?

• A. Lifting a 3-kilogram box 5 meters high
• B. Lifting a 4-kilogram box 4 meters high
• C. Lifting a 5-kilogram box 3 meters high
• D. Lifting a 2-kilogram box 6 meters high

Answer: (B)

The amount of mechanical work required to lift a box straight up against gravity equals W = m g h. Since g is the same for all scenarios, the work scales with the product m × h. Compute m × h for each case: 3×5 = 15, 4×4 = 16, 5×3 = 15, 2×6 = 12. The largest product is 16, so the scenario with a 4-kilogram box lifted 4 meters requires the most work. Numerically, that's about W ≈ 4 × 9.8 × 4 ≈ 156 J, compared to roughly 147 J for the others and about 118 J for the smallest combination.

The amount of mechanical work required to lift a box straight up against gravity equals W = m g h. Since g is the same for all scenarios, the work scales with the product m × h.

Compute m × h for each case: 3×5 = 15, 4×4 = 16, 5×3 = 15, 2×6 = 12. The largest product is 16, so the scenario with a 4-kilogram box lifted 4 meters requires the most work. Numerically, that's about W ≈ 4 × 9.8 × 4 ≈ 156 J, compared to roughly 147 J for the others and about 118 J for the smallest combination.