Collinear but opposite forces (P > Q) Two forces P and Q act along the same straight line but in opposite directions, with P greater than Q. What is the magnitude of the resultant force?
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AP + Q
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BP - Q
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CP / Q
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DQ / P
Answer
Correct Answer: P - Q
Explanation
Introduction / Context:Resultant of collinear forces is found by algebraic addition with appropriate signs. Here, the forces are opposite in sense along the same line.
Given Data / Assumptions:
- P and Q act along one line.
- P > Q and directions are opposite.
- We seek only the magnitude of the resultant.
Concept / Approach:Assign a positive direction; take the algebraic sum. If P is chosen positive and Q acts in the negative sense, the resultant R = P − Q. The direction will be that of the larger force, i.e., along P.
Step-by-Step Solution:
Choose +x along P. Then P = +P, Q = −Q.Algebraic sum: R = P + (−Q) = P − Q.Since P > Q, R > 0, so resultant acts along P.Verification / Alternative check:Vector diagram: two arrows in opposite directions; the smaller cancels part of the larger, leaving difference in the larger’s sense.
Why Other Options Are Wrong:
- P + Q: would apply if both forces acted in the same direction.
- P/Q or Q/P: dimensionally incorrect for a force resultant.
Common Pitfalls:Confusing magnitude with signed result; here only the magnitude is requested, which is the absolute difference.
Final Answer:P - Q