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Chapter 4: Problem 4

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 diagram would display an object with three forces acting upon it: \(\vec{F}_{1}\), \(\vec{F}_{2}\), and \(\vec{F}_{3}\). The first two forces, when combined, produce a resultant force. The third force is equal in magnitude but opposite in direction to this resultant force, thereby causing the net force acting on the object to be zero.

Step by step solution

01

Draw Diagram with Two Forces

Begin by visually representing the problem. Sketch a body and show two arbitrary forces acting on it. The forces should be depicted as arrows stemming from the body, indicating the direction of the forces. The two forces can be labeled as \(\vec{F}_{1}\) and \(\vec{F}_{2}\). Ensure your sketch provides ample space to add a third force.
02

Determine Direction and Magnitude of Third Force

In order for the net force to be zero, the sum of all forces acting on the object should be zero. Thus, the third force must be equal in magnitude but opposite in direction to the resultant of the first two forces. Using the head-to-tail method, add \(\vec{F}_{1}\) and \(\vec{F}_{2}\) to find their resultant. The third force, \(\vec{F}_{3}\), should be drawn in the opposite direction to this resultant, with the same length, indicating it has the same magnitude.
03

Redraw Diagram with Third Force

Add the third force to your diagram. It should be drawn as an arrow starting from the same point as the other forces (\(\vec{F}_{1}\) and \(\vec{F}_{2}\)), but in the opposite direction to the resultant of the first two forces. Make sure you label this new force as \(\vec{F}_{3}\). This completes the diagram with three forces, which results in a net force of zero.

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