Three forces, $(15i + j) \, N$, $(5qi - pj) \, N$ and $(-3pi - qj) \, N$, where $p$ and $q$ are constants, act on a particle - Edexcel - A-Level Maths Mechanics - Question 1 - 2017 - Paper 1
Question 1
Three forces, $(15i + j) \, N$, $(5qi - pj) \, N$ and $(-3pi - qj) \, N$, where $p$ and $q$ are constants, act on a particle. Given that the particle is in equilibri... show full transcript
Worked Solution & Example Answer:Three forces, $(15i + j) \, N$, $(5qi - pj) \, N$ and $(-3pi - qj) \, N$, where $p$ and $q$ are constants, act on a particle - Edexcel - A-Level Maths Mechanics - Question 1 - 2017 - Paper 1
Step 1
Equating the i-components to Zero
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Answer
From the i-components of the forces, we have:
15+5q−3p=0
This simplifies to:
3p−5q=15
Step 2
Equating the j-components to Zero
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Answer
From the j-components of the forces, we have:
1−p−q=0
This simplifies to:
p+q=1
Step 3
Solving the System of Equations
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Answer
Now, we need to solve the two equations:
3p−5q=15
p+q=1
From the second equation, we can express p in terms of q:
p=1−q
Substituting this into the first equation results in:
3(1−q)−5q=15
Solving for q gives:
3−3q−5q=15
ightarrow q = - rac{3}{2}$$
Substituting the value of $q$ back into $$p = 1 - q$$ gives:
$$p = 1 + rac{3}{2} = rac{5}{2}$$
