Component form Definition and 19 Threads

So I was reading the Charles&Wheeler book and this came out of nowhere: but how is it derived in the wholeness?

## \newcommand{\ihat}{\hat{\boldsymbol{\imath}}} \newcommand{\jhat}{\hat{\boldsymbol{\jmath}}} \newcommand{\khat}{\hat{\boldsymbol{k}}} ## Several times now I've seen the following technique for deriving the component form of the dot product. It always felt clean and simple until last night when...

Homework Statement A -12nC charge is located at (x,y) = (1.0cm, 0cm). What are the electric fields at the positions (x,y) = (5.0cm, 0cm), (-5.0cm, 0cm), and (0cm, 5.0cm)? Write each electric field vector in component form. Homework Equations E=k(q/r2) The Attempt at a Solution I was able to...

$\tiny{s6.12.25}$ $\textsf{If $v$ lies in the first quarter and makes an angle }\\$ $\textsf{$\pi/3$ with the positive x-axis and $\left| v \right|$=4} $ $\textsf{find $v$ in component form.}$ \begin{align} \displaystyle v&=\langle 2\sqrt{3},2\rangle \\ \end{align} this is probably correct...

Homework Statement A particle of mass 52[kg] is at 5.0[m]ˆi a particle of mass 13[kg] is at 12[m]j, and a particle of mass 13[kg] is at −12[m]jˆ. What is the gravitational force on the 52[kg] mass due to the mass at 12[m]jˆ? answer: −1.0 × 10−10[N]ˆı + 2.5 × 10−10[N]jˆHomework Equations...

Hello all. Sometimes, when reading a physics book, I find it difficult to distinguish between the magnitud of a vector and the component of a vector. For example, take the weight force, with the positive z direction pointing upwards (that is, F= -mg k). Sometimes, people write F=mg referring to...

How does one derive the general form of the Riemann tensor components when it is defined with respect to the Levi-Civita connection? I assumed it was just a "plug-in and play" situation, however I end up with extra terms that don't agree with the form I've looked up in a book. In a general...

Homework Statement Hi, I need help in solving question c) (a pendulum) The required data, problem and relevant equation is in the pictureThe Attempt at a Solution I am not sure how to solve it but here are my thoughts: since mg is working at j y(t)j= mg does that mean K(r-L0) x(t) direction? I...

Homework Statement Block B has acceleration of 4 m/s2... Relative acceleration of block A w/ respect to B is 4 m/s2. Find magnitude & direction of accel for A? Homework Equations a_A = a_B + a_A/B x_A = x_B + x_A/B y_A = y_B + y_A/B The Attempt at a Solution x & y components: -4cos(20) =...

Homework Statement A 0.17-kg cue ball rests on the pool table. It's struck by a cue stick applying force F1→ = 13Ni^+21Nj^ Determine the magnitude of the ball's acceleration. Homework Equations ax = Fnet, x / m ay = Fnet, y / m a = Fnet / m The Attempt at a Solution Components of...

**refer to attached picture** I'm having some trouble understanding what is happening here. I'm trying to write this vector into its component form so I can solve an equilibrium problem. But I don't understand how the book is splitting this vector. I only drew the vector that I am having trouble...

Angle of vector in component form Find the vector's magnitude and direction. Use right as the +x direction and up as the +y direction. \vec{A} = 3.50 \hat{i} - 7.70 \hat{j} Find \theta_A degrees below the positive x-axis. \theta_A = arctan\left ( \frac{7.70}{3.50} \right )...

Homework Statement First, there is a graph showing x initial at (0,0) and x final at (1,1) Given: F = xy i +xyj Find the work done by this force moving the particle from x initial to x final. [note you'll need a relationship between y and x] Homework Equations W = Fdcos(theta)...

the problem says: find and state the component form of the following vectors. c= 3i + 4j P(0,0),Q(5,-2) for some reason, i think i ended up doing unneccessary work. I found the Work of the problem instead, which is 7. Is work the same thing as component form? If not, what am I supposed to...

Let A = (4.6 m, 20^{}o south of east) How do I write this in compnent form? I know if it were (4.6m, North) is would simply be (0,4.6), but otherwise, how would I calculate this?

Homework Statement A particle moves in the xy-plane with constant acceleration. The particle is located at r= (2i + 4j)m at t=0 s. At t=3 s it is at r=(8i - 2j) m and has a velocity v= ( 5i - 5j) m/s. a) What is the particle's acceleration vector a? b) What are its position, velocity and...

A 2.0 m long wire carries a current of 8.2 A and is immersed within a uniform magnetic field B. When this wire lies along the +x axis, a magnetic force F= (-2.2 j)N acts on the wire, and when it lies on the +y axis, the force is F = (2.2 i -4.2k)N. I saw through inspection that B in the y...

Homework Statement Consider the four charges in Figure P25.46 http://i137.photobucket.com/albums/q208/infinitbelt/p25-46.gif , in which d = 3 cm, q = 4 nC, the +x-axis points to the right, and the +y-axis points up. What is the force on the 1 nC charge at the bottom? Give your answer in...

I am having some trouble figuring out where to start with this problem: The force on a particle of mass m is given by: F= 26i – 12t^2j where F is in N and t in seconds. What will be the change in the particle’s momentum between t=1s and t=2s? Can anyone point me in the right...