# Splitting force vectors into components

Physics is awesome
Hi I am studying force components on a inclined plane. I understand the concept of breaking vectors into X , Y Components relative to the horizontal plane however what I can't seem to make sense of is how the ratios of a triangle and the main input force being the hypotenuse of the triangle allows you to use the ratios of the triangle to determine net force (normal) and the horizontal force. The way I understand it is a triangle is showing the ratios of distance, and when using it with force vectors we are using the same distance ratios to tell us equivalent force in the directions of components (obviously using the ratio of the hypotenuse which is the input force). I see the sides of a triangle as a measure of a ratio of distance traveled so for it to work for force which is a motionless force makes no sense that this would even work. Please elaborate and explain how the ratios of the sides of a tri angle can equate to the ratios of force, when in math we are taught that the ratios of a triangle represent distance of the sides.

Let'sthink
You write, "...I understand the concept of breaking vectors into X , Y Components relative to the horizontal plane ..." That is the second step. First do you understand how vectors add? That is the triangle law and parallelogram law, which are equivalent to each other. We can easily see it to work for displacement vector and by using pulleys, strings and weights one can verify that it works for addition of forces. Once you understand that you would understand that for addition of two vectors give you a unique vector. But if you want to imagine which two vectors will add to a given vector you will have infinite answers as there would infinite parallelograms or infinite triangles whose only one side is given. So we make a special provision by fixing a given direction making an angle theta with the given vector and another direction perpendicular to it and so we deal with only right triangle and rectangle in place of any triangle and any parallelogram.

...for it to work for force which is a motionless force makes no sense...
It works for vectors in general, not just forces. Your question is about math (linear algebra) not physics.

Let'sthink
It works for vectors in general, not just forces. Your question is about math (linear algebra) not physics.
In maths we just define addition of vectors; in Physics we can verify that this mathematics law works for forces and displacements so these physical quantities can be called as vectors. OP may clarify what he refers to as motionless.

Physics is awesome
How is it verified and why does it work for force? A triangle shows distance I guess we are Just suppose to be like blind sheep and believe everything our physics books tell us since no one has a valid explanation of how / why the distance ratios can transfer to force ratios

Staff Emeritus
How is it verified and why does it work for force? A triangle shows distance I guess we are Just suppose to be like blind sheep and believe everything our physics books tell us since no one has a valid explanation of how / why the distance ratios can transfer to force ratios

This is very puzzling.

We draw a vector, or length of a vector, to give a VISUAL REPRESENTATION of the magnitude of the vector. A vector need NOT be drawn at all! I can also represent a vector using a matrix. Would you prefer that?

We draw many things in physics to give us a better visual understanding. When we look at a graph, we are not looking at a "length", we are looking at a visual representation of a quantity, and that maybe the height of the curve represents a value of a quantity.

Zz.

Physics is awesome
Since force is motionless meaning if I am traveling at at a slope of x:3 y:-4 into a plane once I make contact with that plane and create a force there is no distance traveled as in the force going to the right 3 units and down 4 units. What I am saying is how do the lengths ratios (distance) automatically work for force(static force doesn’t have motion, If I push on a desk with 50 N of force my hand isn’t moving) ? The whole concept doesn’t make sense but I guess if we are told it’s true we should believe it.

Staff Emeritus
Since force is motionless meaning if I am traveling at at a slope of x:3 y:-4 into a plane once I make contact with that plane and create a force there is no distance traveled as in the force going to the right 3 units and down 4 units. What I am saying is how do the lengths ratios (distance) automatically work for force(static force doesn’t have motion, If I push on a desk with 50 N of force my hand isn’t moving) ? The whole concept doesn’t make sense but I guess if we are told it’s true we should believe it.

No, your post doesn't make any sense. A "force" doesn't represent motion, nor is it moving or motionless. A force may CAUSE motion. That's a different statement! A "velocity vector" represents motion.

BTW, hang up on the attitude. Assuming you are typing all this on an electronic device and not via telepathy, you are ALREADY believing in many of the things that science says and have produced out of those textbooks. Unless you want to be called ignorant, stop peppering your post with your silly editorial.

Zz.

Physics is awesome
It’s also hard to visually make sense of force because force isn’t something we can see it’s something we can feel. We can’t see something is heavy. So trying to make sense visually on paper is hard because I have no idea really what force is visually explained. So it seems almost impossible to explain the force triangle distance relationship.

Physics is awesome
I don’t have an attitude at all, I don’t get why you wrote that. I am just trying to make sense of something.

...force is motionless...
So is a triangle representing distances. It doesn't imply any motion by itself.

Staff Emeritus
It’s also hard to visually make sense of force because force isn’t something we can see it’s something we can feel. We can’t see something is heavy. So trying to make sense visually on paper is hard because I have no idea really what force is visually explained. So it seems almost impossible to explain the force triangle distance relationship.

But your problem isn't about "force", but rather it appears to be about VECTORS in general! A vector is a vector is a vector! It doesn't matter whether this vector represents displacement, velocity, force, acceleration, electric field, magnetic field, etc...etc. Once a physical quantity is described as a VECTOR, then all the mathematical rules of vectors apply in the SAME way!

So why are you having trouble looking at force as a vector, but not displacement, velocity, acceleration, etc.? If you understand how to apply the vector rules to all those other quantities, why are you having a bump with force?

Zz.

Gold Member
It’s also hard to visually make sense of force because force isn’t something we can see it’s something we can feel.

It's something you can measure, with say a spring scale, and you can definitely see the readings on the scale.

So it seems almost impossible to explain the force triangle distance relationship.

Can you give us a specific example of what you're talking about? Weight is a vector that points vertically downward, by definition. If you resolve it into components that are horizontal and vertical you find that the horizontal component is 0 and the vertical component is ##-mg##. On the other hand, if you resolve into components that are parallel and perpendicular to the ramp you get ##mg \sin\theta## and ##-mg \cos\theta##, respectively.

If the object of mass ##m## moves along the ramp then its motion is parallel to the ramp and so is its acceleration. That is the connection between the force and the motion.
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