Jack_M said:Homework Statement
Find the magnitude and direction of the resultant force Fr=F1+F2+F3 by first finding F'=F1+F2 then Fr=F'+F3
known values are in the link
Homework Equations
Basic vector addition. Law of cosines. Law of sines.
The Attempt at a Solution
Here's my attempt. I'm not convinced by my answer.
http://imgur.com/LcrFApu
BvU said:Hello Jack, welcome to PF :)
F' is just fine.
Fr magnitude is fine too. Check the angle calculation. From your drawing you can already see that 29.12 degrees looks to be too low.
Of course, Quantum D gives a good alternative -- that should be equivalent, but I don't know if that's what the exercise wants you to do.
That's reassuring. Thanks for checking!Quantum Defect said:I get essentially the same numbers that are in the box using x, y vectors: 19 degrees, 29.6 N
My final x components were: +9.7 N x^ direction, +28 N y^ direction -- using inverse tangent gives me 19 degrees from y-axis, as you conclude above.Jack_M said:That's reassuring. Thanks for checking!
A vector addition problem in statics is a mathematical problem that involves adding two or more vectors together. Vectors are quantities that have both magnitude (size) and direction, and they are commonly used to represent forces, velocities, and displacements in physics and engineering.
To solve a vector addition problem in statics, you first need to identify all the given vectors and their magnitudes and directions. Then, use the graphical or analytical method to add the vectors together. The graphical method involves drawing the vectors to scale on a graph and using the parallelogram or triangle rule to find the resultant vector. The analytical method uses trigonometry and the Pythagorean theorem to find the magnitude and direction of the resultant vector.
Scalar addition and vector addition are two different operations in statics. Scalar addition involves adding quantities that have only magnitude, such as mass or temperature. On the other hand, vector addition involves adding quantities that have both magnitude and direction, such as force or velocity. Scalar addition follows the regular rules of arithmetic, while vector addition follows specific graphical or analytical methods.
No, there are different methods for solving vector addition problems in statics depending on the given information. If the vectors are given in component form, you can use the rectangular or Cartesian method. If the vectors are given in magnitude and direction form, you can use the polar or trigonometric method. It is important to understand and choose the appropriate method for each problem.
Vector addition is important in statics because it allows us to accurately represent and analyze physical quantities such as forces, velocities, and displacements. It also helps us to understand the overall effect of multiple forces acting on an object, which is crucial in engineering and physics applications. Additionally, vector addition is a fundamental concept in higher-level mathematics and physics courses.