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Chapter 4: Problem 5

Show two forces acting on an object at rest. Redraw the diagram, then add a third force that results in a net force of zero. Label the new force \(\vec{F}_{3}\).

Short Answer

Expert verified
The third force \(\vec{F}_{3}\) should be added in the opposite direction to the initial resultant force and must be equal in magnitude to retain the zero net force or equilibrium state.

Step by step solution

01

Illustrate Initial Scenario

First off, draw a diagram with an object. Illustrate two forces \(\vec{F}_{1}\) and \(\vec{F}_{2}\) acting on the object. At this moment, the object is in equilibrium, hence the net force on the object is zero.
02

Calculate Resultant Force

Calculate the resultant force due to \(\vec{F}_{1}\) and \(\vec{F}_{2}\). The resultant force \(\vec{R}\) can be determined using the vector summation of force \(\vec{F}_{1}\) and \(\vec{F}_{2}\). In other words, if \(F_{1}\) and \(F_{2}\) are magnitudes of the forces and \(\theta\) is the angle between them then the magnitude of the resultant \(|\vec{R}|\) is given by Pythagorean theorem \(|\vec{R}|= \sqrt{F_{1}^2 + F_{2}^2 + 2F_{1}F_{2}\cos(\theta)}\).
03

Add Third Force

Introduce the third force \(\vec{F}_{3}\) such that the resultant or net force on the object is still zero. Hence, \(\vec{F}_{3}\) must be equal in magnitude and opposite in direction to the initial resultant force \(\vec{R}\). Add \(\vec{F}_{3}\) to the diagram in the opposite direction of the resultant force.

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