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
show that x = 0.75
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Answer
To solve for x, consider the moments about point C:
Using the equation for moments, we have:
M(C)=RDimesx=120imes0.5
where RD is the reaction at D, which is 80 N.
Thus:
80imesx=120imes0.5
Solving for x gives:
x = rac{120 imes 0.5}{80} = 0.75.
Step 2
the weight of the rock
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Answer
Using the equilibrium of moments at point D:
The total moment around point C should be zero for equilibrium:
M(D)=120imes0.25−Wimes1.25
Setting the moments equal gives us:
120imes0.25=Wimes1.25
Solving for W:
W = rac{120 imes 0.25}{1.25} = 24 ext{ N}.
Step 3
the magnitude of the reaction on the plank at D
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Answer
The total weight on the plank is the weight of the plank plus the weight of the rock:
X=W+120=24+120=144extN.
Step 4
State how you have used the model of the rock as a particle
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Answer
In modelling the rock as a particle, I have assumed that its weight acts at a single point (the center of mass) and does not have a significant size or shape. This simplification allows for easier calculations of moments and equilibrium conditions, focusing solely on the gravitational force acting downwards at point B.
