Theory question 118
Statics(a) A body of mass 5kg is placed on a smooth plane inclined at an angle 30° to the horizontal. Find the magnitude of the force; (i) acting parallel to the plane; (ii) required to keep the body in equilibrium. [Take g = 10 ms−2]
(b) A uniform plank PQ of length 10m and mass m kg rests on two supports A and B, where |PA| = |BQ| = 1m. A load of mass 8kg is placed on the plank at point C such that |AC| = 3.5 m. If the reaction at B is 100 N, calculate the (i) value of m; (ii) reaction at A. [Take g = 10ms−2]
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(a)(i) Component of the weight down the plane = mg sin 30° = 5 × 10 × ½ = 25 N
(ii) A force of 25 N up the plane (parallel to it) keeps the body in equilibrium (normal reaction = 50 cos 30° ≈ 43.3 N)
(b) AB = 8 m; the plank's weight 10m N acts at its centre, 4 m from A; the load 80 N acts 3.5 m from A
(i) Moments about A: 100 × 8 = 80 × 3.5 + 10m × 4, so 800 = 280 + 40m, m = 13 kg
(ii) RA + 100 = 80 + 130, so RA = 110 N
On a smooth plane only the weight component along the plane needs balancing; for the plank take moments about one support.