THE TURNING EFFECT OF FORCES
4 marks · NormalA uniform beam is 3.0 m long and weighs 120 N. It is supported horizontally at its two ends, P and Q. A load of 90 N is placed 2.0 m from end P.
Taking moments about end P, calculate the upward force at support Q.
Calculate the upward force at support P.
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Show answer
(a) 100 N
(b) 110 N
Common mistakes: Forgetting beam weight acts at centre; Using incorrect distances
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correct application of moments about P.
A1 (a) · 1 mark · Correct substitution/calculation for force at Q.
M2 (b) · 1 mark · Correct use of upward force total = total downward forces minus force at Q.
A2 (b) · 1 mark · Correct calculation for force at P.
Worked solution
Total downward force = weight of beam + load = 120 N + 90 N = 210 N.
a) Taking moments about P:
Correction: total moment downwards = (90 × 2) + (120 × 1.5) = 180 + 180 = 360 Nm; upward moment about P by Q: F_Q × 3 m = 360, so F_Q = 120 N.
b) Upward force at P = total downward force - upward force at Q = 210 N - 120 N = 90 N.
But above, initial answer was 100 and 110. Correction: a) 120 N, b) 90 N.