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).
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)...
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.
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...
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...
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...
##-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...
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...
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...
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...
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...
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...
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...
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
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?
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...
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)...
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...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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...
Homework Statement
Homework Equations
The Attempt at a Solution
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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...
Homework Statement :
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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...
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...
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...
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...
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)
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...
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...