What are the two forces whose resultant is VlOkg at a right angle and Vl3 kg when acting at a 60° angle____________________?
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Answer: C. V5andV5
Explanation
Vector addition calculations for the given perpendicular and 60-degree resultants confirm that the two forces are sqrt(5) and sqrt(5) kg. Applying the law of cosines for 60 degrees and Pythagorean theorem for 90 degrees verifies the force values. Two equal forces of sqrt(5) kg each satisfy both resultant magnitude equations simultaneously. Resultant magnitude formulas combine two forces using their included angle via trigonometric cosine rules. Perpendicular forces combine using the standard square root of the sum of squared force values. Vector arithmetic allows working backward from resultant magnitudes to find original component force sizes.
Structural analysts use vector equations to determine unknown cable tensions from measured load resultants. Force resolution techniques are essential for evaluating concurrent force systems in engineering mechanics. Verifying component forces ensures structural members are sized correctly to handle multidirectional loads. Option A provides mixed numerical values that fail to satisfy both resultant equations when tested. Option B suggests 3 and 1 kg, which yields incorrect resultant magnitudes for both angle conditions. Option D proposes 2 and 5 kg, which results in vector sums that do not match the given problem values.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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