How Do You Construct a Triangle of Forces?

In summary, the "triangle of forces" (or triforce) is a diagram used to represent the forces acting on an object. The angles of the triangle are determined by the direction of the force vectors, which can be moved around as long as their lengths and directions remain the same. The angles in the triangle can be found using simple trigonometry, and the third angle is always 180 degrees minus the other two angles. Vectors only have length and direction, and can be freely moved around in the diagram.
  • #1
riddle
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What's a "triangle of forces" (triforce, lol)

I've attached a snip from my textbook. I don't get how they make that triangle, and how they get those angles. Can someone please help.
 

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  • #2


The "7 N" force is set to be vertical since it is the gravitational force on an object.
The "A, B, P" diagram shows that vector [itex]T_A[/itex] is at 30 degrees to the horizontal and so is at 90- 30= 60 degrees to the vertical. That's where they get the angle at the bottom of the triangle. The vector [itex]T_B[/itex] is at 40 degrees to the horizontal and so is at 90- 40= 50 degrees to the vertical. That's where they get the angle at the top of the triangle. Of course, the angles in any triangle add to 180 degrees so the third angle in the triangle is 180- 60- 50= 70 degrees, the last angle in the triangle.
 
  • #3


They just translated the force vectors a bit, they drew the Ta force vector at the end of the downward force vector and the Tb force vector at the end of the Ta force vector.

Because the Ta vector makes an angle of 30deg with the horizontal it makes an angel of 90-30=60deg with the vertical. A similar arguments gives the angle of Tb with the vertical
 
  • #4


Oooh. So I guess that these are "free vectors".

EDIT: From Gerbens reply I'll take it as a yes, since they can be moved around.
Thanks guys.
 
  • #5


A vector is a thing that has only length and direction, nothing else.
 
  • #6


riddle said:
Oooh. So I guess that these are "free vectors".

EDIT: From Gerbens reply I'll take it as a yes, since they can be moved around.
Thanks guys.
That is true of all vectors.
 

FAQ: How Do You Construct a Triangle of Forces?

What is a triangle of forces?

A triangle of forces, also known as a triforce or lol, is a graphical representation of the forces acting on an object in a two-dimensional plane. It is used to determine the net force and direction of an object by combining the individual forces acting on it.

How is a triangle of forces drawn?

A triangle of forces is typically drawn by constructing a triangle with each side representing a force vector. The length and direction of each side is determined by the magnitude and direction of the corresponding force. The triangle is then closed by drawing a third side, known as the resultant force, from the end of the first force to the end of the second force.

What is the significance of the angles in a triangle of forces?

The angles in a triangle of forces represent the direction of the forces acting on the object. The angle between the first force and the resultant force is known as the angle of the first force, while the angle between the second force and the resultant force is known as the angle of the second force. These angles can be used to determine the direction of the net force acting on the object.

How is the net force calculated using a triangle of forces?

The net force is calculated by using the Pythagorean theorem to find the magnitude of the resultant force and trigonometric functions to find the direction of the resultant force. The net force is the combination of all the individual forces acting on the object and is represented by the third side of the triangle of forces.

What are some real-life applications of a triangle of forces?

A triangle of forces is commonly used in physics and engineering to analyze and visualize the forces acting on structures or objects. It can also be used in sports, such as in the game of billiards, to determine the direction and magnitude of the forces needed to make a shot. Additionally, understanding triangle of forces can help with navigation and understanding the forces acting on a moving vehicle.

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