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A 1,000 pound boat sits on a ramp inclined at 22°. How much force is pulling down the ramp, and how much force is pressing on a line perpendicular to the ramp?

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sqdancefan

Answer:

  • 374.6 lb down the ramp
  • 927.2 lb perpendicular to the ramp

Step-by-step explanation:

The force due to gravity decomposes into vectors proportional to the sine and cosine of the angle the ramp makes. I find it convenient to remember that when the angle is zero, the full force due to gravity is perpendicular to the ramp. That is ...

  perpendicular force = gravitational force × cosine(ramp angle)

  = 1000 lb × cos(22°) ≈ 927.2 lb

  parallel force = gravitational force × sine(ramp angle)

  = 1000 lb × sin(22°) ≈ 374.6 lb

The boat is being pulled down the ramp by a force of about 374.6 lb, and is pressing perpendicular to the ramp with a force of about 927.2 lb.

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