Parallel forces: like, unlike and the theorem of moments
Answers are for parents and teachers.
1
Like forces of 14 N and 21 N act at A and B, 0.7 m apart. Find R and the distance AC.
R = 35 N. AC = 21 × 0.7 / 35 = 0.42 m (BC = 0.28 m; check 14 × 0.42 = 5.88 = 21 × 0.28).
2
A light pole 1.8 m long has buckets of 60 N and 120 N hung from its ends. Where on the pole should it rest on a shoulder to stay level, and what force does the shoulder give?
The support is at 120 × 1.8 / 180 = 1.2 m from the 60 N end (0.6 m from the 120 N end), and it pushes up with 180 N.
3
A force of 25 N acts upwards at A and 15 N acts downwards at B, with AB = 0.6 m. Find R and where it acts.
R = 10 N upwards. AC = 15 × 0.6 / 10 = 0.9 m beyond A (BC = 1.5 m; check 25 × 0.9 = 22.5 = 15 × 1.5).
4
Upwards positive: 25 N acts upwards at x = 0, 10 N downwards at x = 1 m and 5 N downwards at x = 2 m. Find the resultant and where it acts.
R = 25 − 10 − 5 = 10 N upwards. Σ F x = 0 − 10 − 10 = −20 = 10 xR, so xR = −2 m: R acts 2 m to the left of A.
5
Downward forces of 8 N at A and F at B, with AB = 1.5 m, have a resultant that acts 0.9 m from A. Find F and R.
About A: F × 1.5 = (8 + F) × 0.9, so 1.5F = 7.2 + 0.9F, 0.6F = 7.2 and F = 12 N. R = 20 N downwards.