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. T

    Engineering Determine the resultant of the coplanar forces

    I used Rx = 100cos(0) + 200cos(90) = 100. Ry = 100sin(0) + 200sin(90) = 200. tanO = Ry/Rx = 2. Therefore O(theta) = inv tan (2) = 64 degrees.
  2. theegyptian

    I Brownian motion and the resultant of forces

    Hello, Why isn't the forces resultant on a "large" molecule (by small molecule: water for example) zero? The reason for this Brownian motion is the thermal agitation of the water molecule. If we talk about white and Gaussian noise in electronics (due to the thermal agitation of the electrons)...
  3. S

    Determine the point of application of a resultant force

    I am struggling with part b of the question attached in the screenshot. For part a, I simply add the components of the given forces. I tried calculating the moments using vector cross multiplication, but I don't know what to do after that or even if that step is useful.
  4. G

    Resultant force and centre of pressure in a tank

    Figure: a) CASE A ##\rightarrow p_a=101300\, \textrm{Pa}## $$F_{\textrm{res}}?,\,\, y_c-y_{cg}=y_{cp}$$ We find ##h_{cg}\rightarrow h_{cg}=3+h## $$h=0,75\cdot \sin (30)=0,375\, \textrm{m}\rightarrow h_{cg}=3,375\, \textrm{m}$$ $$p_{cG}=\rho_{H2O}gh_{cg}=33108,75\, \textrm{Pa}$$ We calculate...
  5. D

    Resultant pedal force (FRESULTANT) Force tangential to the crank arm

    %% part 1 clear all; close all; clc; torq_crPK = zeros(10,1); ang_tqPK = zeros(10,1); ang_powPK = zeros(10,1); torq_crDS = zeros(10,1); torq_crUS = zeros(10,1); WD = zeros(10,1); WDpos = zeros(10,1); WDneg = zeros(10,1);%% INPUT VARIABLES for i=1:10 % cyclist number % read in the...
  6. S

    Engineering How to find the sense of rotation of a resultant moment?

    Hello, so I have a question about the sense of rotation of the body. I get the calculating part nd stuff like that. But what I don't understand is how we would determine the sense of rotation about the moment axis? Could someone explain this to me please? (to add to this, I know that it is...
  7. G

    B Resultant force in vertical circular motion

    Suppose we have a vertical circular motion with gravity according to the image below. In the leftmost and rightmost positions the resultant force is pointing diagonally down. Isn't the resultant force supposed to be pointing at the center at all times in a circular motion? What am I getting...
  8. C

    Resultant Frequency and Wavelength of Interfering Sound Waves

    ##-w1## and ##-w2## are to shift the cosine graph to the right, and ##\frac{2pi}{\lambda}## is to stretch the graph. But I can't seem to draw an appropriate ##y1+y2## graph (quite irregular) and I struggle to find the resultant frequency and wavelength. Also, why is there angular frequency in a...
  9. Dom Tesilbirth

    The resultant intensity of two interfering waves

    My Try: The resultant field is given by $$\begin{aligned}\overrightarrow{E}=\overrightarrow{E}_{1}+\overrightarrow{E}_{2}=\widehat{i} E_{0}\cos \omega t+\widehat{j}E_{0}\cos \left( \omega t+\phi \right) \\ \Rightarrow E^{2}=E_{0}^{2}\cos ^{2}\omega t+E_{0}^{2}\cos ^{2}\left( \omega t+\phi...
  10. pairofstrings

    B Adding 'x' to 'xy' for Resultant <=1: A Table Guide

    Hello. How do I add 'x' to 'xy', and the resultant should be <= 1? x + xy = 1 PEMDAS: Step 1: Multiply 'x' and 'y' (2nd term in the equation) Step 2: Add 1st term to 2nd term of the equation Step 1 plus Step 2 should yield value <=1. I know that the curve look like this: 'xy' will give me...
  11. M

    Question about how to calculate the Resultant Force at this point

    Hello all Trying to solve this one, faced a dilemma if i should trasfer the 5N vector from third to first quadrat becuase it head is on the 0 axis ass opposed to the two other vectors. If it remains in third quadrant its components eouls be both negative, if transferred to first quadrant both...
  12. GiriBang

    Resultant of two forces in two different situations

  13. G

    To find the resultant of forces on a lamina

    Could I please ask for help with the following question: A lamina is in the shape of an equilateral triangle ABC, and D, E, F are the midpoints of BC, CA, AB respectively. Forces of magnitude 4N, 8N, 4N, 3N, 3N act along AB, BC, CA, BE, CF respectively, the direction of each force being...
  14. T

    Calculate resultant force of a linear mechanism

    Hi all, I'm currently designing a linear to linear transform mechanism (wedge cam design). Would like to check how much force required to push/ slide the roller down. To ease calculation, i have include some assumption: F2 = 1kg @ maximum compressed angle = 20degree F1 required = ? and how...
  15. G

    To find the magnitude of the resultant of forces around a triangle

    Could I please ask for advice with the following: ABC is a right-angled triangle in which AB = 4a; BC = 3a. Forces of magnitudes P, Q and R act along the directed sides AB, BC and CA respectively. a) Find the ratios P:Q:R if their resultant is a couple. b) If the force along the directed line...
  16. B

    Finding the resultant force using a vector polygon diagram

    Hi I made an attempt at this problem but have got the wrong answer The correct answer is actually resultant force = 21.767 N at 61.34 degrees (or 151.34 degrees bearing), but I don't know how they got that? Any help would be appreciated! Thanks
  17. S

    I How to calculate successive resultant values of a continued fraction

    I understand how these expressions are derived, but I don't see how to calculate successive resultant values. Should the continued fraction expression simply be replaced by 1?
  18. DanchoSuper

    Physics lab report calculating resultant forces -- help please

    i have attached my attempt above i have sent it to my teacher and he said i should fix the mistakes and resend it
  19. P

    To find the resultant intensity

    So I thought of calculating the path differences between all the 3 points by taking them in pairs of 2. S1 and S2 S2 and S3 S3 and S1 I got the path differences as λ/3 , λ and 2λ/3 I can now find their phase differences using the equation Cosx=2π/λ* (path difference) Then I can apply the...
  20. B

    What is the resultant frequency if two similar waves superpose?

    for a) I have ##v = \lambda f= \frac{\omega \lambda}{2 \pi}## for c) and d) I denote ##\frac{2\pi}{\lambda_1} = k_1## and ##\frac{2\pi}{\lambda_2} = k_2## assuming ##k_1 > k_2##. so using the triangular identity I got $$y_1 + y_2 = 2A cos(\frac{k_1+k_2}{2} x - \frac{\omega_1 + \omega_2}{2} t)...
  21. tanaygupta2000

    Resultant field at the center of two semicircular current arcs

    So the magnetic field induced at the center of a current-carrying loop is given by: B = μ0 i /2r where r is the radius of the loop In the case of a semi-circular loop, this becomes B = μ0 i /4r In the question, i = 2A, r1 = 1m and r2 = 2m So, field induced at the center of first semicircular...
  22. D

    Triangle calculation for the resultant velocity

    Top example- How do I get to 31.7 m/s from 30.8 and 7.7? This is way over my head and need help. Thanks in advance Dean
  23. C

    Resultant of two orthogonal vectors

    But the answer in my book is given that sec(theta) =3. Where am I going wrong?
  24. B

    Electric Fields: calculate the resultant force

    Summary:: I try to find the resultant force on "q". I think I have to find the value of Q, but I'm not sure. I Know F1 = k|q * 2Q| / 3² and F2 = k|q * Q| / 2² Hi, this is my first post on this forum I hope I posted in the right section. I try to find the resultant force on "q". I think I...
  25. T

    Why does the resultant Fy have opposite values in my calculations?

    Hello all I was hoping someone could explain why the resultant Fy has a value of +40kN but I get a value of -40kN.
  26. T

    Help With Understanding Resultant Forces By Connecting Vectors

    Hi all I am trying to get my head around resultant forces. I am happy that if I have a vector diagram with 2 forces I can work out graphically the resultant forces by connecting the head of one of the vectors to the tail of the second vector. The confusion comes in when I have 3 or more...
  27. brsclownC

    What is the magnitude of resultant force on a car on a banked curve?

    Ok so I think that the equation for centripetal force is the mv^2/r and this SHOULD equal the horizontal component of the normal force on the car. Vertical component of normal force and gravity would cancel out. However, when I input the numbers into the equations I don't get equivalent values...
  28. T

    Resultant displacement in a stretched spring

    If I take the vector sum, I am getting the angle to be 1. (tan^-1 tan(1)). Is that correct?
  29. S

    Resultant moment of beam fixed at one end

    Hi all, I just wanted to get some clarification on 'resultant moment' when calculated in 2D for a beam which is fixed at one end (point A), and has a load applied at the opposite end (point B). My interpretation of 'resultant moment' would be calculated as sum(M) = Ma + FL, where Ma is the...
  30. Lone Wolf

    Resultant torque of a solid object

    a) ΔK = 1064 = 1/2 * I * (ω²(3) - ω²(2)) I = 2*1064/(ω²(3) - ω²(2)) If I assume α = n*t²: α = dω/dt --> ω = ∫ n* t² dt = n*t³/3 + ω0 = n*t³/3 ω(5) = 100 = n*5³/3 --> n = 2.4 α = 2.4 t² and ω = 2.4 * t³/3 ω(3) = 21.6 rad/s and ω(2) = 6.4 rad/s. Replacing the values: I = 2*1064/(21.6²-6.4²)...
  31. 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)...
  32. OnlinePhysicsTutor

    Resultant amplitude of 6 phasors

    Homework Statement This is a problem from one of my students, he is taking an undergrad module in optics. Most of the question is fine but I cannot see a neat solution to part ii Homework Equations These are the equations for the topic, but I am not sure if we are missing the relevant...
  33. alijan kk

    Find the resultant using the principle of moments

    Homework Statement Homework EquationsThe Attempt at a Solution problem number 10
  34. Taidhg

    Calculate the resultant thrust and overturning moment

    Homework Statement A vertical retaining gate 2metres X 24metres hinged about the bottom edge of a dry dock has water to a depth of 21 metres on one side. Calculate the Retaining Force at the middle of the free upper edge of the gate to keep it shut in the vertical position. With the density of...
  35. Y

    I Resultant of Different Permittivity substances

    Say the space is divided into two parts: one has permittivity e1 and other e2. A charge q1 is placed at a distance d1 from the interface of two media in region in permittivity e1 and another charge q2 is placed at a distance d2 in region of permittivity e2. What is the force experienced by a...
  36. alexi_b

    Finding the angle in which the resultant force points

    Homework Statement Forces of 11.8N north, 19.2N east, and 15.9N south are simultaneously applied to a 3.93kg mass as it rests on an air table. What is the magnitude of its acceleration? What is the direction of the acceleration in degrees? (Take east to be 0 degrees and counterclockwise to be...
  37. 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?
  38. alexi_b

    Map question involving vectors (find the angle)

    Homework Statement Instructions for finding a buried treasure include the following: Go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant...
  39. Frankenstein19

    Fluid Mechanics: resultant force of oil and water on a door

    Homework Statement Homework Equations The Attempt at a Solution [/B] My questions: 1. By resultant force, does that mean the force exerted on the side of the water + force exerted on side of the oil? Because I'd think that the force on the side of the water would be different than the...
  40. G

    B Angle between resultant and vector

    Can we find the angle between resultant and one of its vectors without breaking into components?
  41. H

    Resultant force from water on dam

    Homework Statement : [/B] The cross-sectional profile of a dam is shaped as an isosceles triangle. The dam is standing on horizontal ground and the watermirror is as high as the top of the dam. The dam has height h, length l and the distance from the bottom to the watermirror along the dam's...
  42. A

    I Calculate the Resultant Force Between 4 Points

    I am trying to figure out how to calculate the resultant force between 4 anchor points. Basically I want to hang two kayaks on two ropes suspended across a room. Below I have some crudely drawn images of the set up: I found how to calculate the vector forces between two points as pictured...
  43. T

    Calculating Resultant Load on a Structure with a Tensioned Rope

    Hello all, Can somebody please help me with the following question? I have a rope tied to the top of the building, this drops down vertically 22m onto a balcony which is 15m wide. The rope is then passed over the balcony edge and then hung vertically. The load applied to the rope is 15 kN...
  44. P

    Resultant force of spring at the instant of release?

    Homework Statement What would the resultant force have been at the instant of release, if a 350 g mass were suspended from your spring, pulled down 3 cm and released? What would have been the instantaneous acceleration at the moment of release? The questions pertain to an experiment with a...
  45. 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)
  46. Muhammad Danish

    B Direction of Resultant Force on a Skydiver After Opening Parachute

    When a skydiver falls at terminal velocity, and opens his parachute, what will be the direction of the resultant force immediately after he opens his parachute? As far as I know is that the direction of acceleration will be upwards since his velocity is decreasing. I am a bit confused regarding...
  47. MCTachyon

    Resultant force and its point of action

    Homework Statement A storage tank has the cross-sectional shape shown attached and is of 1m breadth. Calculate the resultant force acting on the inclined surface AB and its point of action. The density of the liquid is 900kgm–3 and take g = 9.81ms–2. Homework Equations P = ρgh F = ρA Point...