Finding Magnitudes of Forces in Similar Triangles

In summary: The magnitude of the second force is yet to be calculated, but it is certainly large. The angles in the triangle are all the same, so the triangle will be similar to a triangle that I draw with the exact same angles. If I know one side, then I use a scale, and we will get the same answer for the lengths. That's the "magic" of similar triangles.
  • #1
afifbaha
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An upward force of magnitude 30N is combined with a second force F which makes an angle of 10degree with the horizontal. The resultant makes an anglre of 40degree with the horizontal.

a. Determine the magnitude of the second force
b. Determine the magnitude of the resultant
 
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  • #2
Where is your attempt?
 
  • #3
rpthomps said:
Where is your attempt?
I have no idea how to do it
 
  • #4
I would start with a sketch of the vectors.
 
  • #5
IN fact if you make a good scale diagram, you could answer the question pretty closely and I think it would give you a good feel for the algebraic approach,
 
  • #6
rpthomps said:
IN fact if you make a good scale diagram, you could answer the question pretty closely and I think it would give you a good feel for the algebraic approach,

Ok this is my diagram. Then what?
 

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  • #7
Well, if you made it to scale, you could just measure the lines now and that would be your answer. But if you are required to come up with an algebraic answer perhaps some trig can help you here. Can you think of some trigonometry that could help you find the sides of that shape?
 
  • #8
rpthomps said:
Well, if you made it to scale, you could just measure the lines now and that would be your answer. But if you are required to come up with an algebraic answer perhaps some trig can help you here. Can you think of some trigonometry that could

help you find the sides of that shape?

How can i draw to scale if i don't know the 2nd force?
 
  • #9
By using a protractor. :)
 
  • #10
Wh
rpthomps said:
By using a protractor. :)

What about the length of 2nd force? The magnitude is yet to be calculated
 
  • #11
As long as the angles in the triangle are all the same, it doesn't matter what the size of the triangle is, it will be similar to a triangle that I draw with the exact same angles. If I know one side, then I use a scale, we will get the same answer for the lengths. That's the "magic" of similar triangles.
 

Related to Finding Magnitudes of Forces in Similar Triangles

1. What are vector components and why are they important in science?

Vector components are the parts that make up a vector, which is a quantity that has both magnitude and direction. In science, vectors are used to describe physical quantities such as velocity, force, and acceleration. Vector components are important because they allow us to break down complex vectors into smaller, more manageable parts for analysis and calculation.

2. How do you solve for vector components?

To solve for vector components, you can use trigonometric functions such as sine, cosine, and tangent. These functions can be used to determine the horizontal and vertical components of a vector, also known as the x-component and y-component. Alternatively, you can also use the Pythagorean theorem and basic algebra to solve for vector components.

3. What is the difference between scalar and vector components?

Scalar components are quantities that only have magnitude, while vector components have both magnitude and direction. Scalar components can be added or subtracted algebraically, while vector components must be added or subtracted using vector addition or subtraction rules.

4. Can vector components be negative?

Yes, vector components can be negative. The direction of a vector component is determined by the angle it makes with a reference axis. If the angle is measured in a clockwise direction, the component will be negative, while an angle measured in a counterclockwise direction will result in a positive component.

5. How are vector components used in real-world applications?

Vector components are used in many real-world applications, including navigation, engineering, and physics. In navigation, vectors are used to determine the speed and direction of movement. In engineering, vector components are used to analyze forces and determine the stability of structures. In physics, vector components are used to solve problems involving motion and forces.

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