Like parallel forces: determine magnitudes from resultant position Two like parallel forces act 24 mm apart; their resultant is 20 N. The resultant's line of action is 6 mm from one of the forces. Find the two forces.
Mechanical Engineering
Engineering Mechanics
Difficulty: Medium
Choose an option
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A15 N and 5 N
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B20 N and 5 N
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C15 N and 15 N
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D10 N and 10 N
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E12 N and 8 N
Answer
Correct Answer: 15 N and 5 N
Explanation
Given data
- Separation d = 24 mm; resultant R = 20 N.
- Resultant is x = 6 mm from one force (take from the smaller unknown without loss of generality).
Concept/Approach
- Along the line joining the forces, position of the resultant satisfies: x = (F2 · d)/(F1 + F2) with R = F1 + F2.
Step-by-step calculation6 = (F2 · 24)/20 → F2 = (6 × 20)/24 = 5 N.F1 = R − F2 = 20 − 5 = 15 N.
VerificationMoment about F1: R × 6 = 120 N·mm equals F2 × 24 = 120 N·mm ✔
Final Answer15 N and 5 N