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Chapter 1: Problem 101

The resultant of two forces equal in magnitude is equal to either of two vectors in magnitude. Find the angle between the forces. (A) \(60^{\circ}\) (B) \(45^{\circ}\) (C) \(90^{\circ}\) (D) \(120^{\circ}\)

Short Answer

Expert verified
The angle between the two forces is \(60^{\circ}\), which corresponds to answer (A).

Step by step solution

01

Define given situation

Two forces, let's call them A and B, have the same magnitude, and their resultant R also has the same magnitude. We will denote the angle between A and B as 胃.
02

Calculate the magnitude of the resultant

Given the magnitudes of A and B are equal, we can denote them as x. To find the magnitude of R, we can use the cosine rule, which is given by: \( R = \sqrt{A^2 + B^2 - 2AB\cos(\theta)}\) Substitute A and B with x and R with x as well: \( x = \sqrt{x^2 + x^2 - 2x^2\cos(\theta)} \)
03

Simplify the equation

Simplify the equation: \( x^2 = x^2 + x^2 - 2x^2\cos(\theta)\) \( 1 = 2 - 2\cos(\theta)\) \( \cos(\theta) = \frac{1}{2}\)
04

Find the angle 胃

As the cosine of 胃 is equal to \( \frac{1}{2} \), we can find the angle using the inverse cosine function: \( \theta = \arccos(\frac{1}{2}) \) The resulting angle 胃 is approximately \(60^{\circ}\)
05

Choose the correct answer

The angle between the two forces is \( 60^{\circ} \), which corresponds to answer (A).

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