Splitting force vectors into components

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• Physics is awesome
In summary, the conversation discusses the concept of breaking vectors into X and Y components and using the ratios of a triangle to determine net force and horizontal force. The importance of understanding how vectors add and the difference between mathematics and physics is also mentioned. The question of how the distance ratios in a triangle can transfer to force ratios is brought up and the need for a visual representation in physics is addressed. It is concluded that while the concept may seem puzzling, it is a valid explanation in physics.

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.

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.

Physics is awesome said:
...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.

A.T. said:
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.

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

Physics is awesome said:
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.

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.

Physics is awesome said:
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.

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.

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.

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

Physics is awesome said:
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.

Physics is awesome said:
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.

Mister T said:
It's something you can measure, with say a spring scale, and you can definitely see the readings on the scale.
Just a thought here — one could take this further and imagine a spring scale connected the corner of a frame containing two orthogonal spring scales which can individually "stretch" only in the "x-" and "y-" directions, respectively. One could then apply a force to the corner scale with some magnitude and direction, which could be verified by the angle and amount of stretch, and then observe what happens to the two orthogonal scales... If this doesn't make sense to the OP, I could sketch up something that illustrates the setup.

Socially force is intrinsically connected with a sense of push and pull and therefore with motion. But the meaning of force in physics is very precise. I do not know whether "Physics is awesome" will understand what I write next directly. But may be others can understand his difficulty and react accordingly. My definition:
"Force is what Newton's laws of motion tell you about it. Nothing more and nothing less." The second statement encompasses all the alternative concepts (or alternative frameworks AFs) students build about force. Nothing less includes those alternative concepts people in general or pupils have are because of not understanding Newton's laws completely. Nothing more type of AFs are because one thinks that he already knows what force is and so does not bother about Newton's laws.

Physics is awesome said:
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

Why do you think a triangle shows distance, I would say it shows the collections of six real numbers, the three sides and three angles. Now these sides could be any thing. let us concentrate only on sides. these can represent distance, speed or magnitude of force. Now if we put arrows they can represent vector quantities such as displacement, velocity and force. This is just representation. Please do not bring your feelings into it. Now you can displace a point or an an object from A to B to C represent these displacements by vector AB, vector BC and final displacement by vector AC and see for yourself the triangle law of addition working for displacements. Think about similar situation of force. for this you would require pulleys weights and strings. You will have to represent forces exerted by strings and Earth on some point by vectors you will have to draw diagrams and verify that triangle law and parallelogram law work for addition of forces as vectors.

1. What is the purpose of splitting force vectors into components?

Splitting force vectors into components allows for a better understanding and analysis of the effects of a force in different directions. It helps to break down a complex force into simpler components that can be individually analyzed.

2. How do you split a force vector into components?

A force vector can be split into components by using trigonometric functions. The component in the x-direction can be found by multiplying the magnitude of the force by the cosine of the angle between the force and the x-axis. Similarly, the component in the y-direction can be found by multiplying the magnitude of the force by the sine of the angle between the force and the y-axis.

3. What are the advantages of splitting force vectors into components?

Splitting force vectors into components allows for a more accurate analysis of forces acting on an object. It also simplifies calculations, making it easier to find the net force and determine the resulting motion of an object.

4. Can a force vector be split into more than two components?

Yes, a force vector can be split into as many components as needed. For example, in three-dimensional space, a force vector can be split into x, y, and z components. This allows for a more comprehensive analysis of forces in all directions.

5. How is splitting force vectors into components related to Newton's laws of motion?

Splitting force vectors into components is closely related to Newton's laws of motion. Newton's first law states that an object will remain at rest or in motion with constant velocity unless acted upon by a net force. Splitting force vectors into components allows us to determine the net force acting on an object in a specific direction, which is essential in understanding its motion according to Newton's laws.