Why Is My Calculation of Force Along a Line Incorrect in Statics?

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SUMMARY

The discussion centers on the miscalculation of force components in a statics problem. The user initially calculated the force using Fcos(tan-1(3/4)), arriving at 320 N, but the correct answer is 420 N. The error stems from only calculating the x component of the force instead of both x and y components for forces AB and CD. To resolve such issues, one must set the sum of the x or y components equal to the corresponding components of the given force.

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  • Understanding of vector components in physics
  • Knowledge of trigonometric functions and their applications
  • Familiarity with static equilibrium conditions
  • Ability to analyze forces in two dimensions
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  • Study the method for resolving forces into components in statics problems
  • Learn about static equilibrium and the conditions for equilibrium in two dimensions
  • Review trigonometric identities and their applications in physics
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Students of physics, engineers, and anyone involved in statics and mechanics who need to accurately calculate force components in two-dimensional systems.

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I have been having trouble with this seemingly easy problem. You would think that it is just as simple as finding Fcos(tan-1(3/4)), which yields the answer 320 N. However, as seen in the image, the actual answer is 420 N.

I would appreciate any help.

Thanks
 
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You've calculated the x component of the given force. That's not what the problem is asking. You need to calculate the x and y components of the forces AB and CD, then set the sum of those x or y components equal to the x or y components, respectively, of the given force.
 

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