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I have the question "Resolve the forces acting on the following objects into their vertical and horizontal components and thus find the vertical and horizontal components of their resultant force."

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Here the vertical component is not given. Only the horizontal is given.

Here is my attempt. I have created a triangle and have used trigonometry to try and find the horizontal and vertical components:

enter image description here

Here I got 3.46 N for the vertical component and 2.0N for the horizontal component. However the solutions say that the resultant force should be 8.0 N.

I am not sure how this is achieved.

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    Resolve ALL the forces into components then sum up the contributions in the vertical (they should add up to zero) and the horizontal (this will get you the answer of 8 N) – 2017-01-18
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    Could you please elaborate. I kind of get it but not completely. – 2017-01-18
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    The thing is you only resolved the upper force, there are three forces and hence three pairs of horizontal and vertical components to consider – 2017-01-18
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    You appear to be consistently misinterpreting these diagrams, having made the same mistake in [another question](http://math.stackexchange.com/q/2103099/265466). There are *three* force vectors in each of the diagrams, some of which have only vertical or horizontal components. – 2017-01-18

2 Answers 2

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Let three forces F1, F2 and F3.

F1 = 4 cos 60° = 2 N

F2 = 4 N

F3 = 4 cos 60° = 2 N

Resultant x component = F1 + F2 + F3.

Hope its help.

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    Sorry I forget to mention its along x component. – 2017-01-18
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Start by defining a suitable coordinate system (this is standard practice in any physics type problem), the most convenient one is with the x and y axes passing through the mass (that is the origin is in the center of the gray circle with the positive y axis pointing up and positive x axis pointing right as usual). Label the three forces $F_1$ the upper force, $F_2$ the middle force, and $F_3$ the lower force. The resultant of a set of forces is the sum of the individual forces $$\text{Resultant Force} = F_1 + F_2 + F_3$$

However these objects are not just numbers but vectors and hence had x and y components, so in order to add them we resort to breaking them up into components (known as vector resolution). You have correctly resolved $F_1$ into it's components so we will also resolve the other two. $F_2$ makes an angle of zero with the x axis and because of this only has a horizontal component of $8$N and a vertical component of $0$N. $F_3$ is the same as $F_1$ except that it points down, it has a positive x component and a negative y component (being in the IV quadrant). You don't need to do any work for this one and can use the previous results for the first force. So the components of $F_3$ are a y component of $-3.46$N and an x component of $2$N. So to add the forces we add their respective components.

$$\text{Resultant y component} = F_{1y}+F_{2y}+ F_{3y} = 3.46\text{N} + 0\text{N} - 3.46\text{N} = 0 \text{N} $$

$$\text{Resultant x component} = F_{1x}+F_{2x}+ F_{3x} = 2\text{N} + 4\text{N} + 2\text{N} = 8 \text{N}$$

The resulting vector only has an x component and so this is the final answer