Practice Exercise S-1.3.1
Central Force Systems - Third Basic Task: Decomposition of a Force
Problem Statement
A force F = 25 N is to be decomposed into two components F1 and F2 which are perpendicular to each other. The lines of action of F and F1 are to form an angle \(\alpha = 35°\).
Determine the magnitudes of F1 and F2 graphically and analytically.
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!
Graphical Solution
Alright, let's figure out the magnitudes of F1 and F2.
Read the problem carefully and create a diagram. This will help you visualize everything important.
Use a Cartesian coordinate system as the basis for the diagram. The common point of application of the forces is the origin (0,0) of the coordinate system.
The position of the force F, which is to be decomposed in this task, is not specified. So, you can initially draw it into the diagram as you wish:
Now you can add the lines of action and the forces F1 and F2 according to the problem statement.
Conditions:
- Forces F1 and F2 are perpendicular to each other.
- The lines of action of F and F1 are to enclose an angle of \(\alpha = 35°\).
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Analytical Solution
To solve this task numerically, it is very helpful to sketch the given information.
Read the task description carefully and draw a sketch. This will help you keep track of all the important information.
Use a Cartesian coordinate system as the basis for the sketch. The common point of application of the forces is the origin (0,0) of the coordinate system.
The position of the force F, which is to be decomposed in this task, is not specified. So you can initially draw it into the sketch as you like:
Now you can add the lines of action and the forces F1 and F2 according to the task description.
Conditions:
- The forces F1 and F2 are at right angles to each other.
- The lines of action of F and F1 are to enclose an angle of \(\alpha = 35°\).
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- Ideal if you need access to already identified content for a short period.
- Unlimited access to all existing and newly created content throughout the entire premium membership.
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Overview of the benefits:
- Cost-effective offer.
- Ideal for short-term exam preparation with the content of TechMechAcademy.
- Unrestricted entry to every piece of content, both existing and newly generated, across the entirety of the premium membership.
- Guaranteed premium membership for one week. Access starts on the day of activation and ends automatically at 0:00 CET (Central European Time) on the following week's day. No cancellation necessary.
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Overview of the benefits:
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- Complete access to all content, both existing and newly produced, under the umbrella of the premium membership.
- Guaranteed premium membership for one month. Access starts on the day of activation and ends automatically at 0:00 CET (Central European Time) on the following month's day. No cancellation necessary.
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Overview of the benefits:
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- Unrestricted admission to all content, both pre-existing and recently generated, within the scope of the premium membership.
- Guaranteed premium membership for three months. Access starts on the day of activation and ends automatically at 0:00 CET (Central European Time) on the following day of the third month from the start date. No cancellation necessary.
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Overview of the benefits:
- Cost-effective due to extended duration.
- Ideal for semester preparation, concurrent semester work, and/or post-semester work with the content of TechMechAcademy.
- Unrestricted entry to a comprehensive collection of both existing and freshly generated content as part of the premium membership.
- Guaranteed premium membership for six months. Access starts on the day of activation and ends automatically at 0:00 CET (Central European Time) on the following day of the sixth month from the start date. No cancellation necessary.
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