What is Coefficient: Definition and 1000 Discussions
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c). When variables appear in the coefficients, they are often called parameters, and must be clearly distinguished from those representing other variables in an expression.
For example,
2
x
2
−
x
+
3
{\displaystyle 2x^{2}-x+3}
, has the real coefficients 2, -1, and 3 respectively, and
a
x
2
+
b
x
+
c
{\displaystyle ax^{2}+bx+c}
, has coefficient parameters a, b, and c respectively assuming x is the variable of the equation.
The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the real coefficient 3 and the parameter represented by c.
Similarly, the coefficient attached to the highest multiplicity of the variable in a polynomial is referred to as the leading coefficient. For example in the expressions above, the leading coefficients are 2 and the parameter represented by a.
The binomial coefficients occur in the expanded form of
(
x
+
y
)
n
{\displaystyle (x+y)^{n}}
, and are tabulated in Pascal's triangle.
Homework Statement
[/B]
(a) Find christoffel symbols and ricci tensor
(b) Find the transformation to the usual flat space form ## g_{\mu v} = diag (-1,1,1,1)##.
Homework EquationsThe Attempt at a Solution
Part(a)
[/B]
I have found the metric to be ## g_{tt} = g^{tt} = -1, g_{xt} = g_{tx} =...
hi,
I'm currently really struggling with an assignment that I've been tasked with.
https://ss1002.files.wordpress.com/2015/01/assignment.pdf
It's mostly theoretical proof questions, which I find difficult. Actual questions I'm fine with.
I have done the first question without issue, as...
[Moderator note: Moved from General Physics so no template.]
An object slides down an inclined plane where there is friction. The time it takes the objects to slide down the plane is 5/4 times longer than the time it takes the same objects to slide down the plane without friction. Calculate the...
Homework Statement
See, I was collecting data for a lab, and now when I look it at, I'm being asked to find the kinetic friction force and the coefficient of friction. What I was given was:
the mass of the block: .261 kg
gravity: 9.81 m/s2
the acceleration: -7.3125 m/s2
And that's it. If it...
Homework Statement
The rectangle in the drawing is held by the horizontal rope and the friction on the wall.
What's the minimal coefficient of friction
Homework Equations
Friction force: f=μN
The Attempt at a Solution
Moments round the point of contact with the wall. the side of the rectangle...
Homework Statement
3 cylinders of mass m and radius 0.5[m]. what is the minimum coefficient of friction between them.
Homework Equations
Friction: f=μN
The Attempt at a Solution
f, the friction force, balances the torque of the weight:
$$mg\cos30^0\cdot0.5\sin30^0=\mu\cdot mg\cos30^0\cdot...
Homework Statement
Consider an uni-dimensional scattering by a delta function at the origin, given by the potential ##V(x) = g \delta(x)##, with ##g>0##.
Using the following result, with ##G(x)## being the green function:
$$\Psi (x) = e^{ikx} + g...
Homework Statement
A skier is sliding down a 20o slope at constant speed, what is the kinetic friction coefficient?
Homework Equations
E = 1/2 mv2
W = Fd
F = ma
F = μN = μmg
The Attempt at a Solution
Attempted to use ma = μmgsin20, which crosses out the masses since mass was not given, but...
Homework Statement
The cylinder weighs 200[N] and lies on a rough surface. a rope holds it in place.
What's the tension T in the rope and what's the minimal coefficient of friction.
Homework Equations
Friction: f=μN
The Attempt at a Solution
All the geometry i have drawn. T balances the...
An air-track glider of mass 0.100 kg is attached to the end of a horizontal air track by a spring with force constant 20.0 N m (Fig. 6.22a). Initially the spring is unstretched and the glider is moving at 1.50 m s to the right.
It is calculated that with an air air track turned off, a glider...
Homework Statement
A rod of mass M and length L is placed horizontally on a table such that the center of mass is a distance L/6 from the edge of the table (CoM is hanging off the table). The rod is released from rest and slips after reaching an angle θ. Find the coefficient of friction \mu
2...
Homework Statement
Picture of Problem:
Homework Equations
$$\psi(x) = A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3
The Attempt at a Solution
I know i need to relate the wave functions $$A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 (the three areas of the barrier - before barrier, inside barrier...
It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure.
It must...
Hello everybody.
I should solve a modified version of second Fick's law in nondimensional spherical coordinates; t is the time and rho [0,1] the nondimensional radius. In this equation the diffusion coefficient is vraiable with t and rho.
The equation is the following:
dC/dt =...
Homework Statement
Flying aircraft X is designed in 2014. The current model has a top speed of 812 m/s, a mass of 72,000 kg when fully loaded, and a maximum thrust to weight ratio of 0.44. Calculate the lifting force and the drag coefficient for the Quinjet when it is flying level at top speed...
Hello all.
I need to design a radiator for 43kw heat dissipation. I have used the LMTD method for finding out the contact surface area of the radiator. But I have a small problem. I cannot find the area unless i know the overall heat transfer coefficient. Can somebody please give an estimate of...
Homework Statement
Just found this site ,looks really helpful , so i am doing some revision using past exam papers and have a few head scratches you guys maybe able to help with .
A car of mass 1000 kg is traveling at a speed of 25 m/s when it applies its brakes suddenly.
The car immediately...
Not sure if I'm getting this right, my answer seems very small, can anyone advise?
Question- butanol at a temperature of 28oC is pumped at a velocity of 14ms-1 through a 100mm diameter tube kept at a wall temp of 90oC. The properties of butanol are below. Determine the convective heat...
So i am working on a program that models the movement of a rocket through different planets. and i sm starting to get teach my self fluid dynamics. As i was reading a presentation by NASA about the forces that act on a rocket they got into shape effects on drag, i noticed from their equation Cd...
Been working on a new way of determining the lift coefficient besides the thin airfoil theory,and I don't know if there is already such a method or if I'm wrong.Plz Help.We know,
L=CL×1/2ρv^2A
Now,as lift is a force,then it should be as L=mμ, where μ is the "upwards acceleration".
So...
Homework Statement
Well it is not the problem itself that bothers me but the maths behind a part of it. As part of finding the coefficient I had to solve the integral of (Sin(x))^(2l+ 1). The solution given by the solution manual just pretty much jumps to the final answer...
The "coefficient of linear expansion" (≡k) was defined in my book by the following relationship:
##\Delta L=Lk\Delta T##
Where L is length and T is temperature
I'm wondering, is this just an approximation? Because, if you were to increase the temperature by \Delta T and then calculate the new...
How do I find the heat transfer coefficient for a meteorite?
The meteorite is made of carboneus chondrite, but approximations with heat transfer coefficients for regular stones or rocky materials would be just as fine.
Furthermore, how would I calculate the energy required to vaporize 1 g of...
I have to make 2 ramps of 30 cm long along with 2 objects(objects need to be 8 cm long). One must be slippery so that it has a low coefficient of friction and one needs to be sticky and have the highest coeffivient of friciton possible. Bassically we place object on ramp raise it from one side...
Homework Statement
I drop a ball downwards vertically onto a smooth table. The coefficient of restitution is 0<e<1. The ball rebounds upwards vertically with speed x. What is the time taken between the time that the ball was dropped to its nth rebound?
Also, what is the time taken before the...
Hi all,
I need to calculate the friction coefficient between road and the tyre of the car.
I came across few answers like which solves as from the following torque equation.
Engine torque = braking torque + acceleration troque + Inertial torque + drag torque + rolling resistance.
For...
Homework Statement
Let p be a prime, k be positive integer, and m ∈ {1, 2, 3, ..., pk-1}. Without using Lucas' theorem, prove that p divides \binom{p^k}{m}.
Homework Equations
The definition of the binomial coefficients: \binom{a}{b} = \frac{a!}{b! (a-b)!}
The Attempt at a Solution
I've...
Hi, I'm new here and I'm having trouble with a question.
1. Homework Statement
A 20.0-kg curling stone is released at the hog line and moves 28.35 m [W] to sit on the button and score a point. If the coefficient of kinetic friction between the stone and the ice is 0.00200, what was the...
Hey guys - I've been using this website to study transmission lines. (great study aid - posting for others to use. Great for smith charts) However, I've noticed this graph they have for load matching:
I'm having trouble finding or understanding a relationship for reflection vs frequency...
I have been investigating the damping of an oscillating mass on a spring by a piece of card of varying surface area, in order to work out the damping constant λ for the equation y = A₀ e-λt sin(ωt). I took the natural log of the amplitude of each successive oscillation and plotting that against...
Hi all. I have some confusion regarding the fugacity coefficient of a species in an ideal solution so hoping someone could clear it up for me. According to my textbook, for fugacity coefficient of a species i in a solution:
So if we...
Hi all,
I want to know the why the Braking force coefficient is increasing first and then decreasing with respect to wheel slip. I attached the graph for your reference
I am using the tyre friction equation Fc=mu*Fnormal to calculate the downforce required for each corner of the Gilles Villeneuve circuit in Canada.
Fnormal composes of the downforce and weight of the car.
mu has a maximum value of 1.7, however this value will vary from corner to corner right...
Homework Statement
I have no values at all, so it's just going to be the variables in the relevant equations. I need to define mu using those variables.
A carousel is moving in a circle at velocity v and has a radius r. It is moving fast enough that each person with mass m is pinned against the...
Does anyone remember/know what the lowest co-efficient is of the imaginary part of the exponent for infinite Riemann zeta sums? I think it's (9/2)*pi, but I'm not sure.
I have tried this question but I seem not to be getting any where.
Qn; An ice-hockey puck is struck from one end of a rink of length 27 m towards the other end. The initial speed is 6m/s, and the puck rebounds from the boundary fence at the other end with a speed which is 0.75 times the speed...
Homework Statement
In the physics lab the following values of a resistor have been recorded as a function of the temperature:
Temperature T/°C
20
30
40
50
60
Resistance R/
213
143
98
69
47It is said that the temperature dependence of R can be described by the following equation...
I'm teaching myself Physics (I really want to study Physics in college), and this is one of the few places where I can ask for help. I hope my questions aren't so silly.
1. Homework Statement
(a) If half of the weight of a small ##1.00×10^3kg## utility truck is supported by its two drive...
Why would the coefficient of kinetic friction be larger for an inclined plane versus a horizontal plane?
Would it be related to the material? I thought initially it was something to do with the force of gravity… but apparently that's not it :(
Thanks so much in advance!
Homework Statement
We're told to find the coefficient of friction for a mousetrap car that we've made, using values that we attained ourselves. We released the arm of the mousetrap onto a scale to find Fa → 1.0*10^2 Newtons.
This is how we found Fa:
m = 1.020kg (←mousetrap held back and...
Homework Statement
The linear prediction of one random variable based on the outcome of another becomes more difficult if noise is present. We model noise as the addition of an uncorrelated random variable. Specifically, assume that we wish to predict ##X## based on observing ##X + N##, where...
Homework Statement
A person pulls a box (m=10 kg) horizontally with +2m/s2 acceleration by applying 45 N force. The displacement of the box is 8 meters from initial position.
a) How much work is done by applied force?
b) How much work is done by kinetic frictional force?
Homework Equations
Wf...
Homework Statement
The surfaces of two blocks are roughened so that they do not slide against each other when a force of 30N is applied to the bottom block. 1.Find the force of friction between the two blocks. 2. Find the minimum coefficient of friction needed between the two blocks so that...
Homework Statement
I got this problem:
A wedge of mass m = 36.1 kg is held in place on a fixed plane that is inclined by an angle θ = 21.3° with respect to the horizontal. A force F = 302.3 N in the horizontal direction pushes on the wedge, as shown in Figure 4.25a. The coefficient of kinetic...
Hey. I am writing my master thesis, and I really need to find the temperature dependent heat capacity and expansion coffient for Cobalt. I have tried searching the internet, whitout luck. Please, can anybody help me. It is really important!
i've been searching for the friction coefficient between medium carbon steels but can't find it,
and also i see everywhere the yield stress of materials but i can't find the compressive stress of materials
Homework Statement
A 1300-kg car is backing out of a parking space at 5.0 m/s . The unobservant driver of a 1700-kg pickup truck is coasting through the parking lot at a speed of 3.2 m/s and runs straight into the rear bumper of the car.
(a). What is the change in internal energy of the...
A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force, FN, and the coefficient of kinetic friction, µk.
So, I know I have to find the vertical and parallel forces
Vertical: Fn and 250 sin of...