To determine whether the forces in each pair are pulling at right angles to each other, we can use the Pythagorean theorem. When two forces (A and B) are perpendicular (at right angles), the resultant force (R) is given by the formula:
\[ R = \sqrt{A^2 + B^2} \]
Now, let's analyze both groups of forces provided.
- First group: 13 lb, 35 lb, resultant force 30 lb
Calculate \( \sqrt{(13^2 + 35^2)} \):
- \( 13^2 = 169 \)
- \( 35^2 = 1225 \)
- \( 13^2 + 35^2 = 169 + 1225 = 1394 \)
- \( R = \sqrt{1394} \approx 37.3 lb \)
Comparing the calculated resultant (approximately 37.3 lb) with the given resultant (30 lb), these forces are not at right angles.
- Second group: 20 lb, 15 lb, resultant force 25 lb
Calculate \( \sqrt{(20^2 + 15^2)} \):
- \( 20^2 = 400 \)
- \( 15^2 = 225 \)
- \( 20^2 + 15^2 = 400 + 225 = 625 \)
- \( R = \sqrt{625} = 25 lb \)
Comparing the calculated resultant (25 lb) with the given resultant (25 lb), these forces are at right angles.
Conclusion:
- The first pair (13 lb and 35 lb with a resultant of 30 lb) are not at right angles.
- The second pair (20 lb and 15 lb with a resultant of 25 lb) are at right angles.
Thus, the correct answer is:
13 lb, 35 lb, resultant force 30 lb no; 20 lb, 15 lb, resultant force 25 lb yes.
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