Practice Exercise S-1.1.4
Central Force Systems - First Basic Task: Reduction to a Single Force
Problem Statement
Picture this: you've got two laundry lines, let's call them Line 1 and Line 2, that you need to attach to a wall. Imagine you're looking down at the setup from above. Something like this:
We know that the force acting on Line 1, which we'll call F1, is 100 Newtons (N).
Determine the force F2 acting on Line 2 in such a way that the combined force, or resultant force, is perpendicular to the wall.
Before You Embark on This Quest: A Pre-Mission Briefing
Before you dive into this adventure, let's do a quick check to see if you're ready for the challenge.
What topic are we dealing with here? Can you explain why?
All the lines of action of the attacking forces intersect at one point. So, we're dealing with a central force system.
If you're not quite familiar with central force systems, no worries! Here are some refresher courses to get you up to speed:
Good luck!
Determining Force F2 to Make the Resultant Perpendicular to the Wall
To determine F2 such that the resultant force R of the two forces is perpendicular to the wall, you first need to carefully read the problem statement.
Draw a sketch where you include all the information from the problem statement.
Use a Cartesian coordinate system for the sketch. The common point of application of the forces is the origin (0,0) of the coordinate system.
Here, you can plot the forces F1, F2 and R. The directions are given by the specified angles 45° and 30°.
Also, include the direction angles of the forces relative to the positive x-axis. You usually need these when solving for a central force system.
Now you’ve got everything in sight!
Since the resultant must be perpendicular to the wall, its y-component must be zero. The resultant thus consists only of its x-component.
Since you don’t know the magnitude of the resultant, use this information to set up an equation.
The y-component of the resultant is calculated according to equation (2.4) with
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