A particle P of mass 2 kg is attached to one end of a light string, the other end of which is attached to a fixed point O - Edexcel - A-Level Maths Mechanics - Question 3 - 2013 - Paper 1
Question 3
A particle P of mass 2 kg is attached to one end of a light string, the other end of which is attached to a fixed point O. The particle is held in equilibrium, with ... show full transcript
Worked Solution & Example Answer:A particle P of mass 2 kg is attached to one end of a light string, the other end of which is attached to a fixed point O - Edexcel - A-Level Maths Mechanics - Question 3 - 2013 - Paper 1
Step 1
Find (i) the value of F
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Answer
To find the value of the force F, we analyze the forces acting on the particle P. We have:
The weight of the particle given by:
W=mg=2extkgimes9.8extm/s2=19.6extN.
In vertical equilibrium, the forces acting vertically must balance:
Timesextcos(30exto)+Fimesextcos(60exto)=2g.
Hence:
Timesextcos(30exto)+Fimesextcos(60exto)=19.6.
The horizontal component must also balance:
Timesextcos(60exto)−Fimesextcos(30exto)=0.
Therefore, we can express T in terms of F and substitute it back to find the numeric value of F.
Step 2
Find (ii) the tension in the string
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Answer
For the tension T in the string:
From our previous equilibrium equations, we can first find F and then substitute back:
Solving the equilibrium equations simultaneously gives:
F=2kgimesextcos(60exto)=2imes9.8imes0.5=9.8extN.
Substituting F into:
ightarrow T = \frac{19.6 - 4.9}{\text{cos}(30)} $$
