Finding components of a force vector given length components of vector

In summary, the problem involves a horseback rider pulling a log with a rope attached, and a force of tension of 2000 N acting along the rope. The length components of the rope are x=1.5m, y=2m, and z=2m, and the problem is 3D with x, y, and z components. Using the equation x^2+y^2+z^2, the length of the rope can be found and the ratios between the components and the length vector can be used to find the force components. The tension acts along the direction of the rope.
  • #1
adam199
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Homework Statement


A horseback rider is pulling a log behind him attached via a rope. The force of tension along the rope is 2000 N. What are the vector components of this force given the length components of the rope? The length components are x=1.5m y=2m z=2m. This problem is 3D so there are x,y,z components.

Homework Equations


x^2+y^2+z^2 equals the length of the rope

The Attempt at a Solution


My guess at the solution to this problem is to find the length of the rope using the lengths of the component vectors, and then using the ratios between these components and the length vector to find the force components.
 
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  • #2
The tension of the rope is in a direction along the line of the rope, so yes, you're right.
 

What is a force vector?

A force vector is a mathematical representation of a force, which includes its magnitude (strength) and direction. It is typically represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction of the force.

How do you find the length components of a force vector?

The length components of a force vector can be found using trigonometric functions. If the angle between the vector and the x-axis is known, the length component in the x-direction can be found using cosine and the length component in the y-direction can be found using sine.

What are the units of a force vector?

The units of a force vector depend on the system of measurement being used. In the International System of Units (SI), the unit of force is Newtons (N), which is equivalent to kg*m/s^2.

How do you find the magnitude of a force vector?

The magnitude of a force vector can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (or the length of a vector) is equal to the sum of the squares of the other two sides (or the length components). In other words, the magnitude is equal to the square root of the sum of the squares of the length components in the x and y directions.

What is the relationship between the length components and the magnitude of a force vector?

The length components of a force vector are directly related to its magnitude. The magnitude is equal to the square root of the sum of the squares of the length components in the x and y directions. Therefore, the longer the length components, the greater the magnitude of the force vector.

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