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 equilibrium, find the value ... 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
Equate the sum of the i components to zero
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Answer
From the forces acting in the i direction, we have:
15+5q−3p=0
This simplifies to:
3p−5q=15
Step 2
Equate the sum of the j components to zero
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Answer
From the forces acting in the j direction, we have:
1−p−q=0
This can be rearranged to:
p+q=1
Step 3
Solve the system of equations for p and q
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Answer
Now we have two equations to solve:
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:
3(1−q)−5q=15
This expands to:
3−3q−5q=15
Simplifying, we get:
3−8q=15
Thus:
ightarrow q = - rac{3}{2}$$
Using this value of q to find p:
$$p + (- rac{3}{2}) = 1$$
$$p = 1 + rac{3}{2} = rac{5}{2}$$
Final values:
$$p = 2.5, ext{ and } q = -1.5$$
