Question

5.
Determine whether the forces in the pair are pulling at right angles to each other.

For each group of three forces below, determine whether the forces in each pair are pulling at right angles to each other.


13 lb, 35 lb, resultant force 30 lb no; 20 lb, 15 lb, resultant force 25 lb no


13 lb, 35 lb, resultant force 30 lb yes; 20 lb, 15 lb, resultant force 25 lb no


13 lb, 35 lb, resultant force 30 lb yes; 20 lb, 15 lb, resultant force 25 lb yes


13 lb, 35 lb, resultant force 30 lb no; 20 lb, 15 lb, resultant force 25 lb yes

Answer 1

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.

1. **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.

2. **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.**