What is Resultant vector: Definition and 46 Discussions

In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. Calculating and visualizing the resultant force on a body is done through computational analysis, or (in the case of sufficiently simple systems) a free body diagram.
The point of application of the resultant force determines its associated torque. The term resultant force should be understood to refer to both the forces and torques acting on a rigid body, which is why some use the term ' resultant force-torque.

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  1. brotherbobby

    The speed of the point of intersection of two uniformly moving lines

    This is the question as it appeared in the text. Attempt : I start by drawing an image of the situation. Two lines 1 and 2 have an angle ##\alpha## between them. The move perpendicular to themselves with velocities ##v_1## and ##v_2##. I am required to find the velocity of their point of...
  2. E

    What is the difference between the two sine rules for resultant vector?

    Hello can anyone help me with this: there are two sine rules for finding the direction of a resultant vector;one for the sides and one for the angle; I tested both formulas and they all worked well and gave me equal answers, does that mean I can use them interchangeably,the rules are: a/sinA =...
  3. Remle

    Vectors Directions: Where is this Resultant Vector Pointing?

    Ok. My problem is what angle to choose when adding vector. Statement does not tell me which one is the "first" force vector. So, when using the law of sine formula I get two results. First, using cosine to get the magnitude: $$\vec c = \sqrt{a^2 + b^2 +2ab\cos\theta},$$ $$\vec c = \sqrt{15^2 +...
  4. Spinnor

    I Resultant vector field as sum of many sources

    Let us have some localized density of sources, S, in a plane, each of which produces a localized circular vector field. Let us work in polar coordinates. Let the density of sources, S = Aexp(-r^2/a^2) and let each source have circular vector field whose strength is given by exp(-(r-r_i)^2/b^2)...
  5. B

    B Force Resultant is equal to the sum of the components -- why?

    Why are the resultant's X and Y components of two forces equal the sum of the X and Y components of the two forces?
  6. Muhammad Danish

    Calculating Resultant Vector: Explained

    According to my understanding, option D is the only possible value of R. I don't understand how options A, B and C are included. Please explain this question. Thanks. (regards)
  7. U

    How does this solution make any sense? (Tension problem)

    I know how to solve this problem with x and y components but how do I solve it with the equilibrant/resultant method? I don't understand how you can make a triangle with both F1 and F2 when in the diagram it looks like the magnitude F1 is only partially represented? Why are we just ignoring the...
  8. V

    Minimum and maximum resultant of three vectors.

    Homework Statement In order to solve a question, I need to find the minimum and maximum resultant of three vectors, their magnitudes are given to me. Homework Equations Magnitude of vector A = 1 Magnitude of vector B = 3 Magnitude of vector A = 5 The Attempt at a Solution The maximum part was...
  9. A

    Darryl drives his load of tomatoes.... (Velocity vectors pic)

    Homework Statement Homework Equations a^2+b^2=c^2 c^2=a^2+b^2-2abCos(theta)The Attempt at a Solution I'm having trouble trying to draw out the vectors. This is my attempt. I feel like it is wrong. Can someone help out please? Also, I'm not sure where to go from here... If I used...
  10. Auburn2017

    Resultant Force and its Components

    Homework Statement The Resultant of the system of forces shown is R = 425 j lbs. Determine the possible values of P and Θ. Homework Equations R = F1 +F2+P The Attempt at a Solution I ended up with two equations, one in the "i" direction and one in the "j" direction. I think you have to use...
  11. R

    B Find resultant vector and equilibrant

    A force, f1, of a magnitude 6 N acts on particle P. A second force, f2, of magnitude 8 N acts at 60 degrees to f1. Determine the resultant and equilibrant of f1 and f2. I use cosine law and found the resultant is 7.2 but the answer is 12.7 I used angle 60 and my solution manual says I had to...
  12. jove8414

    Vector Addition: Find the Resultant Vector

    Homework Statement [/B] The block shown in Fig. P-223 is acted upon by its weight W = 200lb, a horizontal force Q = 600lb and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint...
  13. O

    How do I determine the resultant vector R from R = A + B ?

    Hi everyone, I need steps and some guidance on how to solve questions like this. I know how to do right triangle questions using the Pythagorean method, but when it comes to these non right angle triangles I get so confused. Help! 1. Homework Statement Homework Equations a) The magnitude...
  14. F

    What is the resultant vector electric field at the point P?

    Homework Statement There are 3 charges, each denoted q, the first at (0,a), the second at (0,0) and finally one at (b,0). What is the resultant electric field at point P, (b,a)? Homework Equations E[/B]=q/(4πεo r2) for a point charge The Attempt at a Solution So I know I need to use the...
  15. E

    Resultant Vector Homework: Min Value of |A+B+C|

    Homework Statement Three vectors A, B, C have magnitudes A=5, B=6 and C=7. The minimum value of |A+B+C| is *A represents magnitude, A represents the vector (magnitude and direction) Homework EquationsThe Attempt at a Solution I got 4 because I think that the maximum possible cancellation...
  16. gracy

    Resultant vector physics problem

    angle between two vectors is 90 degrees ,and they are added by parallelogram method ,what will be the angle between resultant and any of the two vectors?shouldn't it be necessarily 45 degrees in such case which i have mentioned i.e when angle between two vectors is 90 degrees
  17. K

    Resultant Vector using Components

    Homework Statement A man pushing a toy car causes it to undergo 2 displacements. The first has a magnitude of 150 cm and makes an angle of 120degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees at the positive x...
  18. A

    Finding the magnitude/direction of a resultant vector?

    Homework Statement Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 20.0 and acts at an angle of 12.9 degrees with respect to the positive x axis. Vector B has magnitude 15.0 and acts at an angle of 55.7 degrees with respect to the positive x axis. Vector C has...
  19. I

    Resultant vector given initial velocity and acceleration

    Homework Statement http://postimage.org/image/466vu4yvp/ http://postimage.org/image/opdrmlv5n/ There can be more than one right answer Homework Equations α=Δv/ΔX v = v0 + αt The Attempt at a Solution Im having difficulty understanding the upward acceleration vector. Because I set the +y...
  20. K

    Resultant vector relative to x and y axis.

    I was wondering if someone could have a look at my attempt at calculating the resultant vector of 3 forces. Figure is here:http://tinypic.com/view.php?pic=2psrllz&s=6, and from the top down the forces are F1=24,9kN, F2=12,7kN and F3=21kN. The angles are(again from the top down) 56,4°, 15,3° and...
  21. S

    Graphically determine resultant vector displacement

    Homework Statement Graphically determine the resultant of the following three vector displacements: 1) 24m, 30 degrees North of East 2) 28m, 37 degrees East of North 3) 20m, 50 degrees South of West Homework Equations The Attempt at a Solution I have the vectors drawn but I...
  22. A

    How do I solve this problem? Finding the resultant vector

    Homework Statement Starting at the origin of coordinates, the following displacements are made in the xy-plane (that is, the displacements are coplanar): 60 mm in the +y-direction, 30 mm in the Ñx-direction, 40 mm at 150°, and 50 mm at 240°. Find the resultant displacement both graphically...
  23. R

    Q: Finding Resultant Forces with Unknown Magnitude and Angle

    Homework Statement Q: Make a scale drawing showing both the forces produced by the cables and the resultant force. Estimate the angle carefully or measure it with a protractor. Supplement: A person with an injured jaw has a brace below his chin. The brace is held in place by two cables...
  24. D

    Calculating Resultant Vector from Angle & Vectors

    Homework Statement Given two vectors(d and e) in the form of (x,y,z), and given the angle between the vectors, how do you find the resultant vector (a) Homework Equations Cosine equation The Attempt at a Solution I know that we can use cosine law some how?
  25. K

    Three Vectors - Resultant vector magnitude?

    Homework Statement Three vectors are shown in the figure (A = 68.0 ; qB = 54.0°). Their magnitudes are given in arbitrary units. What is the magnitude of the resultant vector? Homework Equations here's the image that goes with it The Attempt at a Solution well i figure the angle...
  26. S

    Deriving the standard deviation of a resultant vector

    I am working with some wind speed data and need to work out the standard deviation of the magnitude of the horizontal wind. Unfortunately the only information I have is the standard deviation for the streamwise and cross-stream components of the wind (which are orthogonal). Is it possible to...
  27. T

    Calculating Magnitude of Resultant Vector for X Added to Y = 12i -16j

    Homework Statement Points: 3) A vector X is added to vector Y = 12i -16j. The resultant vector lies along the positive x-axis and has the same magnitude as X. What is the magnitude of X? a. 20.7 b. 16.7 c. 11.3 d. 4.7
  28. D

    Finding Vector with Known Vector and Resultant Vector

    Homework Statement There are two forces. One has a magnitude of 8 N and acts at an angle of 30 degrees on the resultant vector. The resultant vector is 15 N. Homework Equations equations for components (|a|cosx for horizontal and |a|sinx for vertical) cos law and sin law basic trig...
  29. R

    Finding angle for this resultant vector

    Hello I am working on this problem and just can't figure it out... Consider two displacements, one of magnitude 3.0 m and another of magnitude 3.8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 5.7 m, (b) 2.5 m, and (c) 3.6 m...
  30. R

    How Do You Calculate a Drunk Skunk's Displacement?

    Homework Statement In the figure below shows the path taken by a drunk skunk over a level ground, from initial point i to final point f. The angles are θ1 = 30, θ2 = 50, and θ3= 80, and the distance are d1 = 5.00 m, d2 = 8.00 m, and d3 = 12.0 m. What are the (a) magnitude and (b) angle of the...
  31. O

    How do I make the resultant vector equal zero?

    Homework Statement Three forces are applied to an object, as indicated in the drawing. Force 1 has a magnitude of 33.0 Newtons (33.0 N) and is directed 30.0° to the left of the +y axis. Force 2 has a magnitude of 26.0 N and points along the +x axis. What must be the magnitude and direction...
  32. A

    Resultant vector of an isosceles triangle?

    Homework Statement what is the resultant vector of an isosceles triangle? Homework Equations R^2=a^2+b^2-4abcos(theta) The Attempt at a Solution The books answer R=2acos(theta/2) Using the formula above, and knowing that a=b in a isosceles triangle I am getting...
  33. F

    Finding Resultant Vector: A=220g@0°, B=100g@110°, C=160g@260° | Homework Help

    Homework Statement We are given three components: Component A has a magnitude of 220g at 0 degrees, Component B has a magnitude of 100g at 110 degrees, and Component C has a magnitude of 160g at 260 degrees. We are supposed to find the resultant vector. HELP! :) Homework Equations...
  34. 5

    How to Find the Resultant Vector of this Quadrilateral ?

    This question is from a "Solved Problems" book where they give the solutions but I'm not able to get the reason ! Question : ABCD is a quadrilateral.Force BA,BC,CD and DA act at a point.Their resultant is : Options: a. 2AB b. 2DA c. 2BC d. 2BA The given answer is : 2BA Formulas Related...
  35. R

    Finding Resultant Force: Calculation and Explanation

    A person on a parachute has an upwards force of 500N and a downward force of 1000N. The wind strikes the person at 45 degrees and has a force of 300N find the resultant force to 1 decimal place. Hint: Resolve the force of the wind into its horizontal and vertical components, before trying to...
  36. H

    Finding the direction of the resultant vector of three vectors?

    Hi, I was wondering how one would go about finding the direction of the resultant of three vectors, when performing a vector addition of three vectors. I mean I know how to find the magnitude, by summing all the squares of the component vectors, i and j, and square rooting that sum, but how...
  37. C

    The magnitude and the resultant vector

    Hi everyone, Could someone please tell me if the magnitude is the same thing as the resultant vector? I know how to solve for the magnitude, but isn't it the same thing as the resultant vector A+B? Thank you very much
  38. B

    Need help w/ arranging resultant vector with 3 other vectors. D:

    Homework Statement Find the vector combination R = A + 2B - C. Grid lines are separated by 1 cm. When you submit your answer the third vector that you drew may disappear, but if you are correct you will have a green check mark near the grid. (Mac OS X use Netscape, Windows use IE.) A scratch...
  39. C

    Calculate the Resultant Vector of 3D Vectors

    Homework Statement I am having a tough time finding the resultant vector of the the following three dimensional vector: d1x=2.33 cm, d1y= 3.84 cm, d1z= -1.2cm d2x=3.41 cm, d2y= -1.01 cm, d2z = -3.29 cm d3x= -1.04 cm, d3y= 1.93 cm, d3z = 0 cm Find the resultant vector magnitude...
  40. B

    Calculating Resultant Velocity of Airplane in Different Wind Conditions

    Homework Statement **calculate the resultant velocity of an airplane that normally flies at 200km/h if it encounters a 50km/h tailwind. IF it encounters a 50km/h headwind. its obvious that each would either slow down the plane or speed it up but i don't know how
  41. E

    How to calculate resultant vector angle?

    1. A person walks in a path which consists of four straight lines at different angles and lengths as seen in the attached image. http://img253.imageshack.us/img253/244/problemlt5.gif The first part of the problem was to find the resultant displacement which was found to be 512.8. The second...
  42. S

    Need Help With Trig Problem: Finding Resultant Vector

    Hey guys! I feel like I should know how to do this problem from Trig, but I am totally blanking out right now. We have to find the resultant from the vectors that he has given us. One of the vectors is lying on the negative x-axis. How do I find cosine and sine when the line is on the x-axis...
  43. C

    Determine Resultant Vector: Non-90deg Triangle Problem

    Ok I know how to mathematically find the resultant vector in any problem where they form a triangle with an angle of 90 degrees. But what do you do when you don't have a 90deg triangle? The problem: Determine mathematically the resultant of this system of forces F1 (100 N, 30deg) F2 (150 N...
  44. K

    Find the resultant vector made by 115 km at 80 degrees and 85 km at 15 degrees

    I have worked and worked at this problem and it is just not clicking. It is now that I wish geometry would have made sense to me. I am trying to find the resultant vector made by 115 km at 80 degrees and 85 km at 15 degrees. I have been using the graphing method my teacher showed me. I...
  45. T

    Resultant Vector for Two 66m Magnitude Vectors

    what would the resultant vector be for two vectors both 66m in magnitude that look like this: /__ be?
  46. D

    Resultant Vector of magnetic fields

    For what reason is a magnetic force vector perpendicular to the magnetic field vector and the velocity vector of a charged particle? I know F=qvBsin and how to compute cross products but why does the force make a particle move in that particular direction? Is relativity involved?
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