Finding components of a force vector given length components of vector

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SUMMARY

The discussion focuses on calculating the vector components of a force vector given the tension in a rope and its length components in a 3D space. The tension force is specified as 2000 N, with length components of x=1.5m, y=2m, and z=2m. The solution involves using the equation x²+y²+z² to determine the length of the rope, followed by applying the ratios of the length components to the total length to find the respective force components. This method effectively resolves the vector components of the tension force.

PREREQUISITES
  • Understanding of vector components in three-dimensional space
  • Familiarity with tension forces in physics
  • Knowledge of the Pythagorean theorem in three dimensions
  • Basic algebra for solving equations
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  • Study the concept of vector decomposition in physics
  • Learn about tension forces and their applications in mechanics
  • Explore the Pythagorean theorem in three dimensions
  • Practice problems involving force vectors and their components
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Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators looking for examples of force vector calculations in three-dimensional contexts.

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.
 
Physics news on Phys.org
The tension of the rope is in a direction along the line of the rope, so yes, you're right.
 

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