Newton's Second Law in Two Dimensions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Splitting weight on a slope

Mathematics · Mechanics · ages 17-18
Name ______________________   Date ____________

  1. A block slides down a smooth 30 degree slope. Take g = 9.8 m/s squared. What is its acceleration in m/s squared?

    Answer: ______________

  2. A block slides down a smooth slope of angle 30 degrees. Which component of weight pulls it down the slope?

    • mg sin30 degrees
    • mg cos30 degrees
    • mg tan30 degrees
    • mg

  3. A block slides down a smooth slope of angle 30 degrees. Which component of weight pulls it down the slope?

    • mg sin30 degrees
    • mg cos30 degrees
    • mg tan30 degrees

  4. On a smooth slope the normal reaction equals the full weight mg.

    Circle one:   True   False

  5. A 20 N force pulls a sledge at 60 degrees to the direction of travel. What is the forward component in newtons?

    Answer: ______________

  6. Two identical blocks slide down smooth slopes, one at 30 degrees and one at 60 degrees. Which accelerates faster?

    • the 30 degree slope
    • the 60 degree slope
    • both give 4.9 m/s squared

  7. A 4 kg block rests on a smooth 60 degree slope. Take g = 9.8. What is the normal reaction?

    • 39.2 N
    • 9.8 N
    • 19.6 N
    • 4 N

  8. A rope pull angled upward from the direction of travel reduces the normal reaction. True or false?

    Circle one:   True   False

  9. A 5 kg block rests on a smooth 60 degree slope. Take g = 9.8. What is the normal reaction in newtons?

    Answer: ______________

  10. A 4 kg block on a smooth 30 degree slope is pulled up the slope by 30 N. Take g = 9.8. What is the resultant up the slope?

    • 49.6 N up the slope
    • 19.6 N down the slope
    • 30 N up the slope
    • 10.4 N up the slope
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Splitting weight on a slope W1-mt_yNUFF3lxlj-s1

  1. 4.9 · 4.9. Acceleration equals g sin30 degrees = 9.8 times 0.5.
  2. mg sin30 degrees · mg sin30 degrees. The downslope component is opposite the 30 degree angle in the weight triangle.
  3. mg sin30 degrees · The downslope side sits opposite the angle in the weight triangle.
  4. False · Only mg cos(theta) presses in, and cos(theta) is below 1.
  5. 10 · 10. The forward component is 20 cos60 degrees = 20 times 0.5.
  6. the 60 degree slope · Acceleration g sin(theta) grows with steepness toward g.
  7. 19.6 N · 19.6 N. R = mg cos60 degrees = 4 times 9.8 times 0.5.
  8. True · True. The upward component lifts the body, so the ground presses back less.
  9. 24.5 · R = 5 times 9.8 times cos60 degrees = 49 times 0.5.
  10. 10.4 N up the slope · 10.4 N up the slope. Weight pulls 19.6 N downhill, leaving 30 - 19.6 = 10.4 N uphill.
Worksheet · LightMySky