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. lc99

    Replace Loading on Frame By Single Resultant (HW Help)

    Homework Statement Q) Suppose that F1 = 250 lb , F2 = 90 lb , and M = 500 lb⋅ft . (Figure 1) Specify where the resultant’s line of action intersects member BC, measured from B. Homework EquationsThe Attempt at a Solution Okay, so i am having severe problems with figuring out what i did...
  2. 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...
  3. rishi kesh

    Engineering Resultant magnetic flux in a 3-phase induction motor

    Homework Statement I have some attachements below from my textbook. According to it the value of resultant flux is constant in magnitude and 1.5 times the maximum value of flux. But i have a doubt regarding how it is proved. The magnetic flux waveforms are 120° apart from each other and at...
  4. Francis Hannah

    Resultant force-couple system where resultant couple is 0

    For the structure, find the distance from O (in direction OA) to the point where the resultant force-couple system of the forces shown should have a resultant couple of zero. Give answer in metres. a=90 N, b=289 N, c=549 N Clockwise negative, anticlockwise positive. Moment at a =...
  5. EastWindBreaks

    Why must we use integral to find the resultant force?

    Homework Statement Hydrostatic force on a plane surface ex: Hydrostatic force on a gate: Homework Equations The Attempt at a Solution why can't we just use the formula in the red box above for problem 3.57? instead I have to use integral I am confused, how does this gate different from...
  6. F

    How can I draw the resultant force of the couple M, F1 and F2?

    I'm supposed to express the reultant force R of M, F1 and F2 in terms of F1, F2, r, s and α. But I need to know how to draw R first. How can one do this? Does the couple create a force uppwards from O? Can I move F_1 and F_2 also to the origin and combine the forces? Here is the image:
  7. M

    Finding the resultant velocity?

    Homework Statement A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat. Homework Equations None. The Attempt at a Solution I know that the resultant velocity is the hypotenuse...
  8. R

    Resultant Force and Acceleration of Space craft

    Homework Statement https://isaacphysics.org/questions/gcse_ch2_13_q10 https://www.physicsforums.com/attachments/213735 https://i.imgur.com/WnZkt83.jpg The thrust generated by a rocket engine is equal to the mass of propellant burnt each second multiplied by the exhaust velocity of the gas...
  9. X

    2 unknown Forces+known resultant force

    Homework Statement Hi, I'm having trouble with my first mechanics assignment and I'd appreciate some help. So, an object is being pulled using two ropes (Fa and Fb) with a resultant force of 970 N along the x axis. The angle from Fa to the axis is 20 degrees, angle from fb to the axis is 51...
  10. T

    How to calculate resultant force for a bike pedal stroke

    Homework Statement To calculate the resultant pedal force from the variables given: Crank (degrees) measured clockwise from vertical, spindle (degrees) measured anti-clockwise from horizontal, tangent force (N) applied to the pedal surface, normal force (N) applied to the pedal surface and...
  11. lucasLima

    How to find the resultant force in a T tube section

    Homework Statement So, I need to find the X and Y components of the force in the T section Homework Equations Due the fact that the problem dosn't ask for a specific force I couldn't think in any other equation to use, because even tough there is Pressure and Gravity acting I need to...
  12. donaldparida

    Finding the resultant of three vectors

    Homework Statement : [/B]Determine the resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of sides of an equilateral triangle taken in order.Homework Equations : [/B] R2 = A2 + B2 + 2 A B cos θ tan α = B sin θ/(A+B cos θ) The Attempt at a Solution :[/B]...
  13. C

    Finding Resultant Force Using Cosine and Sine Law

    Homework Statement "Calculate the net force with the resultant angle acting on each object indicated in the diagram." The line going off to the southeast is supposed to be straight. My computer art skills aren't great. | 22 N | |_ _ _ _ _ \ ) 35 degrees \ \ 38 N 2...
  14. W

    Resultant Electric field between charges

    Homework Statement A +15 microC point charge Q1 is at a distance of 20 mm from a + 10 microC charge Q2. Fin the resultant electric field at: Ai) the midpoint between the two charges ii) at point P along the line between Q1 and Q2 which is 25 mm from Q1 and 45 mm from Q2. bi) Explain why...
  15. CricK0es

    Resultant of two waves -- Different amplitude+phase difference

    Homework Statement a.) Find the resultant of the two waves: Phasor method E1 = 4cos(ωt) & E2 = 3cos(ωt+\frac{\pi}{2}) b.) By algebraically writing E1 = 4cos(ωt+α-α) & E2 = 3cos(ωt+α+\frac{\pi}{2}-α) Choose α to make the wave have only a cosine termHomework EquationsThe Attempt at a...
  16. M

    Resultant amplitude for waves of different frequencies?

    Homework Statement Two superimposing waves are represented by equations y1= 2sin 2π(10t – 0.4x) y2= 4sin 2π(20t – 0.8x) Find the ratio of Imax and Imin. Ans is (25:9) Homework EquationsThe Attempt at a Solution I know that intensity is proportional to the square of amplitude and maximum...
  17. A

    Resultant equation of two identical out of phase waves

    Homework Statement Two identical traveling waves, moving in the same direction, are out of phase by π/5.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves? (Give the answer as the ratio of the total amplitude to the common...
  18. J

    Magnitude & Direction of Resultant Force & Equilibrant Force

    Homework Statement I need help as to how to find the magnitude and direction of the resultant force, and the equilibrant force. Any and all help is greatly appreciate as I'm stressing myself out over it and I'm not sure what to do. Thanks, Jamie. Homework Equations First question...
  19. dokara97

    Body of mass m is accelerating -- Need to find resultant force

    1. Body of mass m = 3kg is accelerating with acceleration of ##\vec a = 2\vec i + 5\vec j m/s^2 ##. I need to find the resultant force ##\vec F## and the force's value. 2. Of course, the first equation that came to my mind is ##\vec F = m * \vec a## 3. I came with a possible solution for this...
  20. N

    I Resultant force after adding a force to a couple moment?

    I don't get it. Imagine there is a stick leaning aganist a wall. There is a moment couple somewhere on the stick. The end of the stick hits the wall and the wall acts against it. The sum of moment is 0 but since the moment couple forces cancel each other, the resultant force is the wall...
  21. P

    Quick Resultant Forces Question

    Homework Statement So we have 65N @ 30*, 30N @ 180* and 20N at 250* Homework Equations Ncos(angle)i + Nsin(angle)jThe Attempt at a Solution Using this video I did the following. F1(65N) = 65cos(30)i+65sin30i Then using the radian circle I saw that 30* has x,y coordinates of sqrt3/2...
  22. P

    I Question about Resultant Forces

    Alright, so after looking at this video to do it I did the following. F1(65N) = 65cos(30)i+65sin30i Then using the radian circle I saw that 30* has x,y coordinates of sqrt3/2 and 1/2 respectively. So as shown in the video I did 65(root3/2)i+65(1/2)j = 56.3i + 32.5j I did this for the...
  23. T

    Quick question about resultant forces of tugboats

    A ship is being pulled by tugboats with forces of 300 N and 800 N. The angle between the forces is 45 degrees. My question is how can we find the angle between the force vectors and the x-axis? Would it just be 45/2 =22.5 degrees or would it be different because the forces have different...
  24. Z

    Are resultant force and total force the same?

    Homework Statement The wall shown in Fig. 4.28 is 20 ft long. Calculate the total force on the wall due to water pressure and locate the center of pressure Homework Equations Are resultant force and total force the same? The Attempt at a Solution I think they are not the same because resultant...
  25. D

    Calculating the resultant electric field

    Homework Statement In the picture below it is asked that i calculate the resultant electric field if the linear charge density is known. Calculate the resultant electric field of a charged semicircle wire (positioned as in the picture) at some point M on the Z axis if the linear charge density...
  26. J

    Resultant Velocities in 2D (Relativistic)

    Homework Statement Here's the question: http://i.imgur.com/zs130b3.png Homework Equations Just the usual Lorentz transform matrix etc. The Attempt at a Solution http://imgur.com/4Oipfu9 Now, the last line is clearly incorrect, since it tends towards infinite relative speed as v --> c. Of...
  27. 1729

    How Does the Charge Q Affect Forces Between Q1 and Q2?

    Homework Statement A positive point charge Q_1 (4.0 µC) and a negative point charge Q_2 are placed near each other. When a negative charge Q is placed in the middle between the two point charges, the magnitude of the resultant forces on Q_1 and Q_2 doubles. What is the charge of Q? (answer...
  28. Hackerjack

    Vector problem missing magnitude of two vectors

    Homework Statement Force A has a magnitude of 200 lb and points 35deg N of W. Force B points 40deg E of N. Force C points 30deg W of S. The resultant of the three forces has a magnitude of 260 lb and points 85deg S of W. Find the magnitude of forces B and C. Homework Equations...
  29. gracy

    Resultant of two vectors of equal magnitude

    Homework Statement Resultant of two vectors of equal magnitude A is a) √3 A at 60 b) √2 A at 90 c) 2A at 120 d) A at 180 Homework Equations When two vectors are of equal magnitudes then their resultant is ##A_R## = 2 A Cos θ/2 The Attempt at a Solution I think we need more information...
  30. gracy

    Resultant of Forces Can Equal Zero: 1,2,3,4?

    Homework Statement Resultant of which of a following may be equal to zero? 1)10 N, 10 N , 10N 2) 10 N, 10 N , 25 N 3) 10 N, 10 N , 35N 4)None of these More than one option can be correct. Homework Equations Addition of vectors The Attempt at a Solution 1) Resultant of these three forces can...
  31. 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...
  32. S

    Maximum angle between resultant and original vector

    Homework Statement Two vectors of magnitude 5 units and 3 units are added such that the angle between the resultant and the vector of magnitude 5units is maximum. Find this angle. Homework EquationsThe Attempt at a Solution Knowing that the resultant vector makes a smaller angle with a...
  33. Designman

    Resultant angle of a suspended body after torque is applied

    A body in an absolute vacuum is suspended from an axle having no friction at the body or at the suspension points. A power source is affixed to the body which rotates the axle. At rest the body is horizontal. The body weighs 4000 lbs. The center of gravity of the body is vertically 4 ft. below...
  34. P

    Resultant Displacement with direction problem

    Homework Statement You run towards the west with a velocity of 4 m/s for 5 minutes. You then continue running to the northeast (halfway between north and east) at 2 m/s for 8 minutes. (a) At the end of the 13 minute run , what was your total running distance? (b) At the end of the 13 minute...
  35. 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...
  36. F

    What is the Direction of Resultant Force on a Stationary Vane Caused by Water?

    Homework Statement in the calculation , the direction of resultant force that we got is the force of vane act on water , right ? to get the resultant force act on vane ? it should be opposite to the force of vane act on water , am i right ? IMO , the resultant force at stationary vane (which is...
  37. F

    Is the direction of resultant force to the left in this problem?

    Homework Statement i am confused about the direction of resultant force . in the working ,it's clear that the author taking to the right as positive , for the force component along x-axis , we have -Fx , but , in the calclulation , we gt positive 32230N , so the resultant force of x-component...
  38. F

    Resultant force at elbow from water flow

    Homework Statement water flows in an elbow was aligned horizontally , of angle 135 degree . If the water volume is section 1 and 2 is 0.2m^3 , the elbow is 12kg , flow rate is 0.4(m^3)/s , find the resultant force Homework EquationsThe Attempt at a Solution i found x and y component of the...
  39. W

    Direction of resultant force

    Homework Statement why the resultant force on blade is acted downwards (toward A)? why shouldn't it be slanted upwards ? since the horizontal component of the force acted 2.12kN to the left , and 0.735kN upwards , we would get the resultant force acting slanted upwards , right ? Homework...
  40. M

    Calculate the average resultant force required to accelerate the ball.

    Homework Statement A 56 g tennis ball is accelerated at 1000 m s-2 to reach its service velocity. Calculate the average resultant force required to accelerate the ball. Homework Equations F = MA The Attempt at a Solution Mass = 0.56g = 0.056kg Acceleration = 1000m/s2 0.056 x 1000 = 56N...
  41. J

    What is the resultant of the vector from this impact?

    Homework Statement two people kick a ball. one of them kicks it with a force of 215.0 Newtons. the other one with 189.0 Newtons. their approach creates a 210.0 degree angle at the point of impact and causes the ball to go in a different direction. what is the resultant of the vector from this...
  42. P

    Determining the magnitude of the resultant couple

    Homework Statement Calculate the magnitude and coordinate angles of the resultant couple moment, caused by the forces. Homework Equations M= r x F The Attempt at a Solution M3= -0.2* 80k= -16k M2= 0.2* 120i= 24i M1= -0.2*100j= -20j M4= r x F= ? I just can't seem to be able to expres r into a...
  43. x2017

    Resultant Impulse Homework: ΣFΔt = mΔv

    Homework Statement Homework Equations ΣFΔt = impulse mΔv = momentum ΣFΔt = mΔv The Attempt at a Solution I got the first part of the question (I hope I did it correctly), I just don't understand what my professor means by resultant impulse... Do I use the same equation? Is it going to be...
  44. Priyadarshini

    Circular Motion and resultant force

    Homework Statement Homework Equations F= mv^2/r v = angular vel* r The Attempt at a Solution resultant force= ma-frictional force = mv^2/r - mg*meu = (angular vel)^2mx - mg*meu But then how do I get the angular speed when I don;2 know the resultant...
  45. S

    STATICS problem: Minimum Resultant Force

    Problem Statement: If the resultant force acting on the bracket is required to be a minimum, determine the magnitude of F1 and the resultant force. Set ∅=30 deg. I have found the components of each force and set them up into a resultant vector, with F1 solved symbolically into its...
  46. G

    Equivalent Resultant Force for Distributed Load: Is My Method Correct?

    Homework Statement i am asked to find the equivalent resultant force for this question . for the distributed load , i divided into 4 parts , is my method correct? Homework EquationsThe Attempt at a Solution total force about y = 6sin30 + 3(3) + (5-3)(0.5)(3) + 5(4) + (7-5)(4)(0.5) total...
  47. D

    How large is the resultant force on Gavin's toy car after he kicks it?

    Homework Statement Gavin is kicking one of his toy cars with a force straight ahead. the car weighs 1.2 kg and has friction free wheels so that the friction forces of the car is small when it has started. Gavin kicks his car with the force of 2.4 N. How large is the resultant force? Homework...
  48. P

    Determine the resultant displacement

    Homework Statement Using the superposition principle, determine the resultant displacement of the particles in the medium, at the instant shown. Homework EquationsThe Attempt at a Solution
  49. T

    Finding the resultant of coplanar forces problem

    Homework Statement A uniform ladder of weight W rests with its top against a rough wall and its foot on rough ground which slopes down from the base of the wall at 10 degrees to the horizontal. Resolve, horizontally and vertically, each of the forces acting on the ladder. Homework...
  50. O

    Upward and Resultant Velocity

    1. You launch a projectile from a wall that is 2 meters in height. It lands on the ground 2 seconds later. -What is the initial upward velocity of the projectile at the moment of launch? -What is the initial resultant velocity of the projectile at the moment of launch?2. Equations given: - v =...
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