THE TURNING EFFECT OF FORCES
4 marks · NormalA uniform plank of wood is 4.0 m long and has a weight of 200 N. It rests horizontally on two supports placed 0.5 m from each end.
Calculate the distance from Support 1 to the centre of gravity of the plank.
Determine, using the principle of moments about Support 1, the upward force at Support 2.
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(a) 1.5 m
(b) 62.5 N
Common mistakes: Forgetting plank's weight acts at centre; Miscalculating distances
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Correct distance from support 1 to centre: 2.0 m - 0.5 m = 1.5 m
M1 (b) · 1 mark · Applies principle of moments about Support 1
M2 (b) · 1 mark · Uses weight at correct distance and total moments
A2 (b) · 1 mark · Correct final value for upward force at Support 2
Worked solution
a) Plank is 4.0 m; centre is at 2.0 m. Support 1 is at 0.5 m, so distance from Support 1 to centre = 2.0 m - 0.5 m = 1.5 m.
b) Let S2 be force at Support 2, which is 30 m from Support 1 (actually, since scale is ×10, 35 - 5 = 30, but 4.0 m plank, support at 0.5 m and 3.5 m, so distance between supports is 3.5 - 0.5 = 3.0 m).