Question

Use the prompt below for questions #7-10:
Three different families, each driving a 2000kg rental minivan, decide to drive to a ski resort for winter break that is at the top of a 700m hill. The first family takes Route A, the second family takes Route B, and the third family takes Route C.
7. How much force does it take to get up to the ski resort?
8. How much work does it take the family traveling on Route B to get to the ski resort if they travel 1,150m?
9. How much work does it take the family traveling on Route C to the ski resort if they travel 940m?
10. If Route A is just over 700m, did the family that took Route A use more, less, or the same amount of work to get to the ski resort as the family that took Route B? Explain.

Answer 1

7. The weight of the van is the force needed to lift it vertically: F = mg = 2000 kg × 9.8 m/s² = 19,600 N.
(If moving along an incline of length L, the force along the slope to overcome gravity is F = mg(h/L).)

8. Work (gravity) for Route B = mgΔh = 2000×9.8×700 = 13,720,000 J ≈ 1.37×10^7 J.
(If you prefer using force along the slope: FB = mg·(700/1150) ≈ 1.19×10^4 N, and W = FB×1150 = 1.37×10^7 J.)

9. Work for Route C = mgΔh = 2000×9.8×700 = 13,720,000 J ≈ 1.37×10^7 J.
(Along-slope force FC = mg·(700/940) ≈ 1.46×10^4 N, and W = FC×940 = 1.37×10^7 J.)

10. Same amount of work. Ignoring friction and other losses, the work against gravity depends only on the vertical rise (mgh), so any path from base to the 700 m higher resort requires the same work. (If friction/rolling resistance are included, longer routes could require more total work.)