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

Question

12 lb, 13 lb, resultant force 19 lb no;  15 lb, 36 lb, resultant force 39 lb no

 

12 lb, 13 lb, resultant force 19 lb yes;  15 lb, 36 lb, resultant force 39 lb no

 

12 lb, 13 lb, resultant force 19 lb yes;  15 lb, 36 lb, resultant force 39 lb yes

 

12 lb, 13 lb, resultant force 19 lb no;  15 lb, 36 lb, resultant force 39 lb yes

Answer 1

Answer: Based on the calculations, none of the given options result in forces that are pulling at right angles to each other.

Let's evaluate each group of forces:

1. 12 lb, 13 lb, resultant force 19 lb Using the Pythagorean theorem: 122+132=144+169=313122+132=144+169=313 313≈17.69313​≈17.69
2. The magnitudes of the given forces do not add up to the magnitude of the resultant force (19 lb). Therefore, the forces are not at right angles to each other.
3. 15 lb, 36 lb, resultant force 39 lb Using the Pythagorean theorem: 152+362=225+1296=1521152+362=225+1296=1521 1521=391521​=39
4. The magnitudes of the given forces (15 lb and 36 lb) add up to the magnitude of the resultant force (39 lb). However, this does not necessarily mean the forces are at right angles to each other; they could be pulling in the same direction.
5. 12 lb, 13 lb, resultant force 19 lb Using the Pythagorean theorem: 122+132=144+169=313122+132=144+169=313 313≈17.69313​≈17.69
6. The magnitudes of the given forces do not add up to the magnitude of the resultant force (19 lb). Therefore, the forces are not at right angles to each other.
7. 15 lb, 36 lb, resultant force 39 lb Using the Pythagorean theorem: 152+362=225+1296=1521152+362=225+1296=1521 1521=391521​=39
8. The magnitudes of the given forces (15 lb and 36 lb) add up to the magnitude of the resultant force (39 lb). However, this does not necessarily mean the forces are at right angles to each other; they could be pulling in the same direction.

Based on the calculations, none of the given options result in forces that are pulling at right angles to each other.