To determine whether the forces in each pair are pulling at right angles to each other, we can use the Pythagorean theorem. If two forces are perpendicular, the relationship for the magnitude of the resultant force \( R \) is given by:
\[ R = \sqrt{A^2 + B^2} \]
Where \( A \) and \( B \) are the magnitudes of the two forces.
Analyzing the Groups
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For Forces of 13 lb and 35 lb with Resultant 30 lb:
- Calculate \( R \) for this pair:
\( R = \sqrt{(13^2 + 35^2)} = \sqrt{(169 + 1225)} = \sqrt{1394} \) - Since \( \sqrt{1394} \) is not equal to 30 lb, this indicates that these forces are not perpendicular.
- Calculate \( R \) for this pair:
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For Forces of 20 lb and 15 lb with Resultant 25 lb:
- Calculate \( R \) for this pair:
\( R = \sqrt{(20^2 + 15^2)} = \sqrt{(400 + 225)} = \sqrt{625} = 25 \text{ lb} \) - The calculated resultant matches, indicating that these forces are perpendicular.
- Calculate \( R \) for this pair:
Conclusion
Based on the analysis above:
- The first pair (13 lb, 35 lb) is not pulling at right angles.
- The second pair (20 lb, 15 lb) is pulling at right angles.
Thus, the answer is: 13 lb, 35 lb, resultant force 30 lb no; 20 lb, 15 lb, resultant force 25 lb yes.