A bench consists of a plank which is resting in a horizontal position on two thin vertical legs - Edexcel - A-Level Maths Mechanics - Question 4 - 2009 - Paper 1
Question 4
A bench consists of a plank which is resting in a horizontal position on two thin vertical legs. The plank is modelled as a uniform rod $P S$ of length 2.4 m and mas... show full transcript
Worked Solution & Example Answer:A bench consists of a plank which is resting in a horizontal position on two thin vertical legs - Edexcel - A-Level Maths Mechanics - Question 4 - 2009 - Paper 1
Step 1
(a) the magnitude of the normal reaction between the plank and the leg at Q and the magnitude of the normal reaction between the plank and the leg at R
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Answer
Let the normal reactions at points Q and R be denoted as C and D respectively.
Using the equilibrium condition of moments about point R:
C+D=120extN
Now applying the moment about Q:
M(Q)=80gimes0.8+40gimes0.4−40gimes0.4=Dimes1.6
This simplifies to:
D=30g
From the first equation, we then have:
C=90g
Thus, the normal reactions are:
At Q: C=90g N
At R: D=30g N.
Step 2
(b) find the distance QX
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Answer
Let the normal reaction at Q when Arthur sits at X be 2F and at R be F.
Applying the equilibrium condition:
2F+F=40g+20g+60g
Now setting the moment about point Q:
M(Q)=60gimes20g+20gimes0.4=40gimes0.4+Fimes1.6
From this setup, we can derive:
QX = rac{16}{15} ext{ m} ext{ or } 1.07 ext{ m}.
