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2-1 (g) Theoretical results

2-1 (g) Theoretical results

Point 7 of 12 — Parallel Coplanar Forces: Resultant and EquilibriumQuestion bank: 0 questions (0 with pictures)

07 2-1 (g) Theoretical results

Moving one of two like forces

✍️ Worked examples

Example 9:

  • Like forces F1 and F2 act at A and B with resultant R.
  • If F2 moves parallel to itself a distance x along AB, prove that the resultant moves a distance F2F1+F2x in the same direction.

Solution:

  • Moments about A: R⋅AC=F2⋅AB.
  • After the move the point of action of F2 is B′ with AB′=AB+x, and the resultant acts at C′: R⋅AC′=F2⋅AB′.
  • Subtract: R (AC′−AC)=F2 x, so CC′=F2Rx=F2F1+F2x.

Forces given as vectors

✍️ Worked examples

Example 10: F⃗1=2i^−3j^ acts at A(1,3) and F⃗2=4i^−6j^ acts at B(4,9). Find the resultant and the point where its line of action meets AB.

Solution:

  • R⃗=F⃗1+F⃗2=6i^−9j^.
  • F⃗2=2F⃗1, so the forces are parallel and in the same direction.
  • ACCB=F2F1=21, so C divides AB in the ratio 2:1 from A.
  • C=(2(4)+1(1)3,2(9)+1(3)3)=(3,7).

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