A uniform plank AB has weight 120 N and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1
Question 2
A uniform plank AB has weight 120 N and length 3 m. The plank rests horizontally in equilibrium on two smooth supports C and D, where AC = 1 m and CD = x m, as shown... show full transcript
Worked Solution & Example Answer:A uniform plank AB has weight 120 N and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1
Step 1
(a) show that x = 0.75
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Answer
To determine the value of x, we can use moments about point C. Taking moments about C gives:
M(C)=80imesx=120imes0.5
Solving for x:
80x=60
x = rac{60}{80} = 0.75
Step 2
(b) the weight of the rock,
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Answer
When the rock is placed at B, the plank is at the point of tilting about D. Using moments at point D:
Assuming the reaction at C is 0:
M(D)=120imes0.25−Wimes1.25
Setting this equal to 0 gives:
120imes0.25=Wimes1.25
Solving for W:
W = rac{30}{1.25} = 24 ext{ N}
Step 3
(c) the magnitude of the reaction of the support on the plank at D.
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Answer
The total weight acting downward is the weight of the rock plus the weight of the plank:
X=24+120=144extN
Step 4
(d) State how you have used the model of the rock as a particle.
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Answer
The weight of the rock acts precisely at B, and by modelling it as a particle, we can assume that all its weight is concentrated at that point, which simplifies the calculations of moments and forces in the system.
