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Chapter 2: Problem 268

Out of the following pairs of forces, the resultant of which can not be $18 \mathrm{~N}$ (A) \(11 \mathrm{~N}, 7 \mathrm{~N}\) (B) \(11 \mathrm{~N}, 8 \mathrm{~N}\) (C) \(11 \mathrm{~N}, 29 \mathrm{~N}\) (D) \(11 \mathrm{~N}, 5 \mathrm{~N}\)

Short Answer

Expert verified
The pair of forces for which the resultant cannot be 18 N is (D) 11 N and 5 N, as the range of magnitudes for this pair is [6 N, 16 N], which does not include 18 N.

Step by step solution

01

Pair A: 11 N and 7 N

To find the maximum possible magnitude of the resultant force, we can add the two forces directly (11 N + 7 N = 18 N). For the minimum magnitude, we can subtract the smaller force from the larger one (11 N - 7 N = 4 N). In this case, the possible range of resultant force magnitudes is [4 N, 18 N]. So 18 N is a possible resultant force for pair A.
02

Pair B: 11 N and 8 N

For this pair, the maximum possible magnitude of the resultant force is obtained by adding the two forces (11 N + 8 N = 19 N). To find the minimum magnitude, we can subtract the smaller force from the larger one (11 N - 8 N = 3 N). In this case, the range of magnitudes is [3 N, 19 N], so 18 N is also a possible resultant force for pair B.
03

Pair C: 11 N and 29 N

For pair C, we add the forces to find the maximum possible magnitude (11 N + 29 N = 40 N). For the minimum magnitude, subtract the smaller force from the larger one (29 N - 11 N = 18 N). In this case, the range of magnitudes is [18 N, 40 N]. So 18 N is a possible resultant force for pair C.
04

Pair D: 11 N and 5 N

For the last pair, we add the forces to find the maximum possible magnitude (11 N + 5 N = 16 N). To find the minimum magnitude, we can subtract the smaller force from the larger one (11 N - 5 N = 6 N). Here, the range of magnitudes is [6 N, 16 N]. In this case, 18 N is not within the range of possible magnitudes, so Pair D is the answer. The pair of forces for which the resultant cannot be 18 N is (D) 11 N and 5 N.

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