Explanations & Calculations
- Resolution of forces is normally done into 2 components orthogonal to each other.
- The component resolved into the side of the given angle is written with a cosine: F×cosθ.
- Then the other component (which is normal to the previous component) can be obtained with a sine: F×sinθ.
- When the angle between the force and the x-axis is obtuse or reflex (they form acute angles as well), you can try these 2 to resolve components,
- use the angle without thinking so much in the formulae of resolution.
- find the acute angle and resolve with that angle.
For the first situation,
Falong x-axisFalong y-axis=(11×104N)×cos33=9.23×104N=(11×104N)×sin33=5.99×104N
The procedure is the same for the second situation as the angle is acute.
For the third situation,
Falong x-axisFalong y-axis=11.3kN×cos193=−11.01kN⋯(along negative x-axis)=11.3kN×sin193=−2.54kN⋯(along negative y-axis)
- From the acute angle's point of view,
- The acute angle here is 193−180=130
- Now you can visualize the alignment of the force with the x-axis, it is so close to the negative side and the components will also be along negative axes.
- Then the resolution looks like this,
Falong (-) x-axisFalong (-) y-axis =11.3×cos13=11.01kN=11.3×sin13=2.54kN
- In the first case, you are notified of this behaviour with a negative sign in prefix to the values.
This is the same procedure for the fourth case as well and the acute lies below the positive x-axis.
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