What is Resultant: Definition and 512 Discussions

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant.The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation.
The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's resultant for distinguishing it from the usual resultant) is a generalization, introduced by Macaulay, of the usual resultant. It is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).

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  1. A

    Resultant force on a pulley system

    Homework Statement Could anyone give me an idea of how to start this problem to work out the resultant force's magnitude, direction and couple in the top (alternator) pulley? Does the 30° angle affect the equations? As all the notes I have seem to only have pulleys with the force at each...
  2. 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...
  3. B

    Find the resultant of these two force vectors using the following methods.

    Homework Statement Find the resultant of the following vectors using these methods: triangle method, parallelogram method and mathematical method. Fa is a force vector with magnitude of 10.0N and makes an angle of 25.0 degrees with the x-axis. Fb is a force vector with a magnitude of 5.0N...
  4. M

    Resultant Torque independent of origin?

    Homework Statement Let a system of forces (F1,...Fn) act on a body at points (x1,...xn) respectively. Assume that the resultant or net force vanishes (sum of forces = 0) Show that the resultant torque of this system is independent of the choice of origin, i.e. for 2 different origins x0...
  5. ME_student

    Resultant Vectors and Equilibriant Vectors

    Question: How do the Equilibrant and Resultant vectors relate to each other? My answer: They relate to each other because they are both vectors. Equlibrant is when forces are equal, but opposite each other, thus brings an object to an equilibriam state. A resultant vector is two or more vectors...
  6. M

    Showing resultant stresses on a volume element

    Me again, (this is what happens when you make a designer do mechanics, and give her a lecturer she doesn't understand :P ). I'm stuck on a combined loadings question. This is the question: "The 60 mm diameter rod (fixed at end C on the wall) is subjected to the loads shown. 1) Transform...
  7. 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...
  8. 9

    Question regarding the elevator acceleration resultant force

    Question regarding the "elevator" acceleration resultant force Homework Statement In the "elevator" case, when a man is standing on a weighing scale, and the elevator accelerate upwards, the resultant force acting on the man will be UPWARD force, and the man is feeling "HEAVIER". So here is...
  9. O

    Balancing Moments: Solving for Distance in a Force System Resultant

    Homework Statement http://i.imgur.com/NcI8y.png?1 So i did A and got the answer of Fr to be {-129i, -221j} N and the Mra = -354k Nm which are right from the answer key so now about part b I think I should balance all moment at the G point about z axis or something like that thus...
  10. M

    Resultant Force on an object during Non-Uniform Motion

    Homework Statement A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m), as shown. At an instant when θ = 50°, the tension in the string is 8.0 N. What is the magnitude of the resultant force on the mass at this instant...
  11. B

    Resultant of three forces about a point O

    My question is to find the resultant just take the x,y components of each force, find the magnitude by squaring them and taking the square root. My question is after doing that how would i find the perpendicular and horizontal distances. My teacher put a study guide for our test and it said...
  12. I

    Net force from a straight-line resultant?

    1.Two concurrent forces act on a box. The first force acts east at 13 Newtons and the second force acts west at 17 Newtons. What is the net force acting on the box? >Draw each vector using the tip to tail method. >Draw your resultant and label it "R" >With your ruler determine the...
  13. V

    Calculating resultant velocity

    An airplane has an air speed of 4.20 × 10^2 km/h [N 45° E]. The wind speed is 30 km/h to the west. a) What is the airplane’s resultant velocity? I decided to use the trigonometric solution, but I am confused on how to break the equation down in order to get 399 km/h c2 = a2 + b2 - 2ab.cosC c2...
  14. N

    Determine x and y coordinates of resultant force through object

    Homework Statement The concrete slab supports the six vertical loads shown. Determine the x- and y-coordinates of the point on the slab through with the resultant of the loading system passes. Image attached Homework Equations The Attempt at a Solution I started off by...
  15. A

    Calculating resultant force of friction from rope and bar.

    Hello, I hope this is a suitable forum, it's a million miles from homework but it may be on the same sort of level. A picture is worth a thousand words so please have a look at the attached picture. When the rope is pulled there isn't just the issue of gravity, but also of the friction of...
  16. E

    Calculating the Resultant Force on a Gate - Is No Force at B Possible?

    I've figured out the resultant force on the gate by adding the magnitudes of F1, F2, and F3. However, I'm trying to figure out the distance b such that there is absolutely no force acting on the stop at point B. Is this even possible? It seems like it isn't, since all forces are pointing to the...
  17. C

    Finding the resultant of 3 Vectors modeling a force table

    Hey, sorry for the basic question, but I'm curious. Can one create a resultant for 2 vectors that cannot be drawn head- to - tail, and are facing opposing directions? The idea is that I set up a force table and took measurements on how many Newtons of force are acting upon each spring...
  18. N

    Force Couple System and resultant force

    Homework Statement Replace the force-couple system at point O by a single force. Specify the coordinate yA of the point on the y-axis through which the line of action of this resultant force passes. Homework Equations The Attempt at a Solution I'm not sure how to start this...
  19. C

    Statics: Determine the magnitude of the resultant force

    [b]1. Homework Statement : The Attempt at a Solution I keep attempting this problem and so far I have got this: F1x: 150 F1y:260 F2x:424 F2y:424 F3x:600 F3y:250 Then I add the x's together and y's together, square both and take the square root for magnitude, but can't seem...
  20. B

    How Do You Calculate Displacement from Dallas to Chicago Using Vector Addition?

    Homework Statement A map suggests that Atlanta is d1 = 730 mi in a direction of θ1 = 5.12° north of east from Dallas. The same map shows that Chicago is d2 = 559 miles in a direction of θ2 = 21.0° west of north from Atlanta. Modeling the Earth as flat, use this information to find the...
  21. C

    Resultant force from three forces.

    Homework Statement http://session.masteringengineering.com/problemAsset/1127110/6/Probs.2-39_40.jpg I will refer to this picture for the problem. I have to find the resultant of the three force vectors. I know all except F1 and theta. I am given it for this problem to find the resultant...
  22. U

    Resultant force projected along a line

    Homework Statement (i) Find the resultant force acting at point D and write it in Cartesian form. (Note that CD is parallel to the y-axis, the 40N force acts parallel to the z-axis and the 30N force is parallel to the x-axis.) (ii) Find the magnitude of the projected component of the...
  23. P

    Resultant Velocity of sailing boat

    Homework Statement A boat is sailing on a bearing of 120° and has a speed of 4ms^-1 relative to water. A current has a speed of 2ms^-1 and flows south west. Find the resultant speed of the boat 2. The attempt at a solution I've been stuck on this question for an hour now and can't...
  24. G

    Spring Force Resultant help please

    Hey guys, how are you? I feel so stupid right now, I'm having a hard time getting my mind straight, which of the two resultant force diagram on the right is right? Typically its a slider with a ball and spring that slides on a recess (cam type). I want to know the force required on the slider...
  25. C

    Resultant gravitational field strength

    Homework Statement Consider the objects X and Y, each of mass 8000kg and 2000m apart where XYP forms an equilateral triangle. Determine the resultant gravitational field strength at point P due to objects X and Y. Homework Equations G= GM/R^2 The Attempt at a Solution
  26. A

    Finding the resultant force on the block

    Homework Statement Hi all, I've been given a question for homework and I am not 100% sure how to do it exactly! I have included a diagram or the situation Homework Equations The question is Find the resultant force on the block (picture attached) The Attempt at a Solution What i did...
  27. J

    5-point star resultant force question

    Any help on where I start with this question. Need to convert each force into its horizontal and vertical components, but don't know any angles apart from the 70N force acting straight down.
  28. Z

    Classical Potential Barriers and their Resultant Forces

    So, I'm writing a code to solve Hamilton's equations for a free classical particle incident on different potential barriers in 1D. I'm eventually going to be using this for some sort of semi-classical analysis, but for now have to get this working as expected. I first tested it using a...
  29. P

    Calculating Resultant Vectors Using Trig

    Given Info: 4 m/s [N30°E] and 5 m/s [S17°E]. FIND: The Resultant Vector And it's angle.So I'm having a big problem with figuring the angles between the two vectors... I feel like I'm doing it correctly, but at the same time I'm not sure... Here's my diagram. http://i47.tinypic.com/x38osl.jpg So...
  30. H

    Resultant velocities from 2D collision

    Homework Statement Suppose you have two 2D circles, where size ≈ mass, each of which is moving with known x- and y-velocities. The two collide, not necessarily head-on (one could broadside the other, etc). How do I calculate the resultant velocities, assuming no elasticity or friction...
  31. Rococo

    Adding waves to get resultant wave

    Homework Statement I need to show that the waves: sin((kx)+(θ/2)) and sin((kx)-(θ/2)), differing in phase by θ, add to give a resultant wave 2sin(kx)cos(θ). But the answer I get is different so I'm not sure how to do this. Homework Equations sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)...
  32. F

    Finding the magnitude of the resultant vectors

    I need help on how to solve this Homework Statement Three vectors, expressed in Cartesian coordinates are : S -> x( -3.5), y(+4.5) T -> x(0), y(-6.5) U -> x(+5.5), y(-2.5) what is the magnitude of the resultant vector S + T + U? The answer, according to my answer sheet is 4.9...
  33. C

    Why is the resultant electric field pointed like this?

    Heres the question: Two charges (one is +4μC, the other is -8μC). They lie on 80mm apart, so you can imagine that the +4μC charge is on the left and the -8μC is on the right. Point P is equidistant from the two charges, draw two arrows at P to represent the directions and relative magnitudes of...
  34. M

    Resolving forces and finding from the resultant

    Homework Statement Three forces: F1, F2 and the other with a magnitude of 40 N act on the ring bolt as shown in Fig. C.1. The resultant, R, has a magnitude of R = 180 N and acts at an angle of 80° anti-clockwise from the x-axis. Determine the magnitudes of F1 and F2. Homework Equations...
  35. N

    Conservation of momentum: Student walking on surfboard find resultant velocity

    Homework Statement A 55 kg student stands on a 4.6 kg surfboard moving at 2.0 m/s [E]. The student then walks with a velocity of 1.9 m/s [E] relative to the surfboard, relative to the water. Neglect Friction. Answer: 0.25 m/s[E] Homework Equations m1vi1 + m2vi2 = m1vf1 + m2vf2 The...
  36. S

    What is the difference between relative velocity and resultant velocity?

    relative velocity and resultant velocity?also in a connected(with strings) pulley system,how can we calculate the acceleration and velocities of the pullies and the masses connected onto it?
  37. B

    Components of A Resultant Force

    The following problem is one I have contrived by my own ability, so if there is any error please let me know. Say I have a box, with a chain attached at one of the edges of the box, and I apply 10 N pull at a 40° angle with the surface of the box. Now I know we sometimes resolve vectors into...
  38. R

    Finding the Angle of Resultant Force in a Plane

    Homework Statement I am having quite an issue solving this resultant force question: The following forces act on a point in the same plane: 40N direction due north; 10N direction due east, 40N direction 50° south of west, 20N direction northwest and 15N direction 20° south of east...
  39. S

    Calculation of % component of resultant force

    Hi everyone, This appears to be a trivial question but I'm uncertain to the correct answer. If I have forces of 3N, 4N and 5N in the x,y and z directions respectively. The resultant force will be the square root of these components squared ≈ 7N. If I want to describe any of the components...
  40. M

    Applying principle of superposition to draw resultant shapes. Please help

    Homework Statement Apply the principle of superposition to draw the resultant shape when each of the sets of pulses shown interferes. (Draw the diagrams so that the horizontal midpoints of the pulses coincide.) Homework Equations Please check this website...
  41. J

    Noted and corrected, thank you!

    Homework Statement a boat heads north at 3.4 m s^-1 across a river that flows East at 1.6 m s ^-1. 1)Calculate the resultant velocity of the boat and the time taken to cross the river which is 180 m wide. 2)What is the distance traveled from its starting point when the boat reaches the...
  42. F

    Determining phase of resultant from partial interference of waves

    When you have waves that are out of phase by some fraction of a cycle, e.g not exactly in phase and not exactly 180 degrees anti-phase, how do you determine the phase (relative to the original component waveforms) of the resultant? Specifically, is there an equation that solves for phase...
  43. Femme_physics

    Resultant vectors in cable and beams

    I know that when I have cable connected, the resultant vector of each cable will point at the direction of the angle it's connected in. http://img26.imageshack.us/img26/8454/wiresn.jpg BUT, suppose we switch all these cables to rigid body structures like beams. I cannot make the same...
  44. F

    Superposition of light waves: 90 degrees out of phase, amplitude of resultant?

    Two waves are perfectly superposed (traveling same direction), but are 90 degrees out of phase. Does this result in destructive or constructive interference, as the waves could be seen as either half anti-phase or half in-phase. For example, the first wave has an amplitude of 1. The second wave...
  45. N

    Moments and the line of action of the resultant force

    Homework Statement Homework Equations ƩMoments = Moment + Fx*d + Fy*d R = (Fx)i + (Fy)j The Attempt at a Solution I'm only interested in part (ii) I calculated the components of the resultant force and they are |R| = 1.15(i) + 9.36(j) I know that the x-intercept of line of action...
  46. C

    Question: How do I accurately calculate the resultant of 3 vector inputs?

    I have just been given my first assignment and I have calculated all the data, but there is no clear writing that says what answer they want. Im sorry if this is a stupid question but i have just started physics, anyway i have been given three forces which had to be converted to cartesian...
  47. P

    Find Resultant Force of F1,3 & F2,3 | .899 N Magnitude

    I need to find the resultant force for two separate forces - F1,3 and F2,3. F1,3's components are x= -.719 and y= -.54. F2,3's components are x= .719 and y= -.54. The angle between the q1-q3 line and the x-axis is 36.9. F1,3 and F2,3's magnitude is .899 N. Can someone help me?
  48. M

    Vectors and resultant vectors?

    Homework Statement An airplane starting from airport A flies 300 km east, then 350 km at 30.0" west of north, and then 150 km north to arrive finally at airport B. The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this...
  49. M

    How do I find the tension and angles in a spider's web?

    Homework Statement A spider is resting after starting to spin its web. The gravitational force on the spider is 0.165 N on the junction of three strands of silk. The junction is supported by different tension forces in the two strands above it so that the resultant force on the junction...
  50. S

    Resultant forces of coplanar systems

    Homework Statement Determine the magnitude of F if the resultant of the three forces passes through point O. Homework Equations ƩFx = 0 ƩFy = 0 ƩM = 0 The Attempt at a Solution The most I can come up with is that the two forces on the left would equal F on the right, and...
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