   Chapter 11.1, Problem 79E

Chapter
Section
Textbook Problem

# Think About It Consider two forces of equal magnitude acting on a point.(a) When the magnitude of the resultant is the sum of the magnitudes of the two forces, make a conjecture about the angle between the forces.(b) When the resultant of the forces is 0, make a conjecture about the angle between the forces.(c) Can the magnitude of the resultant be greater than the sum of the magnitudes of the two forces? Explain.

(a)

To determine

To calculate: The angle between the two forces when the magnitude of the resultant of two forces of equal magnitude is the sum of the magnitude of the two forces.

Explanation

Given:

The magnitude of resultant of two forces of equal magnitude is the sum of the magnitude of the two forces.

Formula used:

The magnitude of resultant of twoforces a and b is given by a2+b2+2abcosθ.

Algebraic identity (a+b)2=a2+b2+2ab.

Calculation:

Let the two forces be u and v.

The magnitude of the resultant of these two forcesis u2+v2+2uvcosθ.

As provided in the question, the magnitude of resultant of two forces of equal magnitude is the sum of the magnitude of the two forces

(b)

To determine

To calculate: The angle between the two forces when the resultant of two forces of equal magnitude is zero.

(c)

To determine

The magnitude of the resultant can be greater than the sum of the magnitude of these two equal forces.

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