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 val... 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
The equation for the i components is given by:
15+5q−3p=0
This simplifies to:
5q−3p=−15
Step 2
Equate the sum of the j components to zero
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Answer
The equation for the j components is given by:
1−p−q=0
This can be rearranged to:
p+q=1
Step 3
Solve the system of equations
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Answer
We now have the following two equations to solve:
5q−3p=−15
p+q=1
Substituting equation 2 into equation 1, we find:
5(1−p)−3p=−15
This simplifies to:
5−5p−3p=−15−8p=−20
Thus,
p=2.5
Substituting the value of p back into equation 2:
2.5+q=1
Solving this yields:
q=1−2.5=−1.5
