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Physics Lesson 4.1.4 - Expressing Forces in Components
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Welcome to our Physics lesson on Expressing Forces in Components, this is the fourth lesson of our suite of physics lessons covering the topic of What Causes Motion? The Meaning of Force, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Expressing Forces in Components
When two or more forces acting at the same object are neither in the same direction nor in the opposite, it is better to express them in components. Then, after calculating the resultant force in each direction, the Pythagorean Theorem is used to calculate the magnitude of the resultant force. Let's illustrate this point by a numerical example.
Example 2
Calculate the resultant force F⃗R acting at the object in the figure.
Solution 2
From the figure, we can see that 1 unit = 4 N.
First, let's express all forces in components. We have two directions involved here: the horizontal (or x-direction) and the vertical (y-direction). Also, we take left as negative and right as positive in the horizontal direction and up as positive and down as negative in the vertical direction. Therefore, we can write:
F1y = ( + 6) units × 4 N/unit = + 24 N
F2x = ( + 2) units × 4 N/unit = + 8 N
F2y = (-4) units × 4 N/unit = -16 N
F3x = (-6) units × 4 N/unit = -24 N
F3y = (-2) units × 4 N/unit = -8 N
Thus, we have for the resultant forces of the each direction
= ( + 16)N + ( + 8)N + (-24)N
= 0
FRy = F1y + F2y + F3y
= ( + 24)N + (-16)N + (-8)N
= 0
In this case, there is no need to calculate the total resultant force because it is obvious it is zero (the object remains at rest). However, in the general case, we would write
= √02 + 02
= 0
Remark! When the object is voluminous as the one in the specific example, we take the force vectors as acting at the centre of the object.
You have reached the end of Physics lesson 4.1.4 Expressing Forces in Components. There are 4 lessons in this physics tutorial covering What Causes Motion? The Meaning of Force, you can access all the lessons from this tutorial below.
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