Forces as Vectors: Resolving and Resultants · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Splitting and adding forces

Mathematics · Mechanics · ages 16-17
Name ______________________   Date ____________

  1. A 20 N force acts at 30 degrees above the horizontal. What is its vertical component in N?

    Answer: ______________

  2. A 20 N force acts at 30 degrees above the horizontal. What is its vertical component in N?

    Answer: ______________

  3. A 10 N force acts at 60 degrees to the horizontal. What is its horizontal component?

    • 8.7 N
    • 10 N
    • 5 N

  4. A 3 N force pulls east and a 4 N force pulls north on the same object. What is the size of the resultant?

    • 5 N
    • 7 N
    • 12 N

  5. Sam draws a free body diagram of a book showing gravity, the normal force, and the push of the book on the table. He says all three belong. Is Sam right?

    Circle one:   True   False

  6. A 5 N force pulls east and a 5 N force pulls north. What is the direction of the resultant?

    • 45 degrees north of east
    • 30 degrees north of east
    • 60 degrees north of east
    • Due north

  7. A 10 N force acts at 60 degrees to the horizontal. What is its horizontal component?

    • 5 N
    • 8.7 N
    • 10 N
    • 2.5 N

  8. A 6 N force pulls east and an 8 N force pulls north. Give the magnitude of the resultant in N.

    Answer: ______________

  9. Jo resolves a 20 N force at 30 degrees and claims 10 N across and 17.3 N up. Is Jo right?

    • No, sine and cosine are swapped: across is 17.3 N, up is 10 N
    • Yes, both parts are exactly as Jo says
    • No, both parts must equal 10 N

  10. A 3 N force pulls east and a 4 N force pulls north. What is the direction of the resultant?

    • 53 degrees north of east
    • 37 degrees north of east
    • 53 degrees east of north
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Answer key

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

Splitting and adding forces W1-mt_-qDRgd2g8v-s1

  1. 10 · Vertical part is 20 sin 30 = 20 times 0.5 = 10 N.
  2. 10 · The vertical part is 20 times sin 30, which is 20 times 0.5.
  3. 5 N · The horizontal part is 10 times cos 60, which is 10 times 0.5.
  4. 5 N · The forces are perpendicular, so the resultant is root 25, which is 5.
  5. False · The push of the book on the table acts on the table, so it must be left out.
  6. 45 degrees north of east · Equal components give tan θ = 1, so θ = 45 degrees north of east.
  7. 5 N · Horizontal part is 10 cos 60 = 10 times 0.5 = 5 N.
  8. 10 · Root 36 plus 64 is root 100, which is 10.
  9. No, sine and cosine are swapped: across is 17.3 N, up is 10 N · Cosine sits beside the angle, so across is 20 times cos 30, about 17.3.
  10. 53 degrees north of east · tan is 4 over 3, about 1.33, and the angle with that tan is about 53 degrees.
Worksheet · LightMySky