answers

watching

views

26 Nov 2019

Two vectors are A = 6x + 4y +3z and B = 2x - 3y -3z;

(a)What is the projection of A along the x, y, z directions,respectively?

(b)What are the scalars components of B?

(c) What are the vector components of A and B?

(d) What can you conclude about the vector -B, when comparedto B? Express it in terms of vector components.

(e) Construct a 3-D Cartesian system, label the axes (assignnumerical values like 1,2,3, etc, for each axis) and draw thevectors A and B.

(f) Determine A + B in terms of vector components as well asmagnitude and direction.

(G) Determine A - B in terms of vector component as well asmagnitude and direction.

answers

watching

views

For unlimited access to Homework Help, a Homework+ subscription is required.

Related questions

A circular loop of wire with area A lies in the xy -plane. As viewed along the z -axis looking in the -z -direction toward the origin, a current I is circulating clockwise around the loop. The torque produced by an external magnetic field B is given by , where is a positive constant, and for this orientation of the loop the magnetic potential energy is negative. The magnitude of the magnetic field is .

a) Determine the vector magnetic moment of the current loop. Express your answer in terms of the variables , , , , and .

b) Determine the component of B.

c) Determine the component of B.

d) Determine the component of B.

cerisehare907

A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time is plotted on the horizontal axis and velocity on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call the velocity and the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively. Here is a plot of velocity versus time for a particle that travels along a straight line with a varying velocity. Refer to this plot to answer the following question.

What is the average acceleration of the particle over the first 20.0 seconds?

beigecrow871

A force F⃗ of magnitude F making an angle θ with the x-axis is applied to a particle located along the axis of rotation A, at Cartesian coordinates (0,0) in the figure. The vector F⃗ lies in the XY plane, and the four axes of rotation A, B, C, and D all lie perpendicular to the XY plane. (Figure 1)

A particle is located at a vector position r⃗ with respect to an axis of rotation (thus r⃗ points from the axis to the point at which the particle is located). The magnitude of the torque τ about this axis due to a force F⃗ acting on the particle is given by

τ=rFsin(α)=(moment arm)⋅F=rF⊥,

where α is the angle between r⃗ and F⃗ , r is the magnitude of r⃗ , F is the magnitude of F⃗ , the component of r⃗ that is perpendicular to F⃗ is the moment arm, and F⊥ is the component of the force that is perpendicular to r⃗ .

Sign convention: You will need to determine the sign by analyzing the direction of the rotation that the torque would tend to produce. Recall that negative torque about an axis corresponds to clockwise rotation.

In this problem, you must express the angle α in the above equation in terms of θ, ϕ, and/or π when entering your answers. Keep in mind that π=180degrees and (π/2)=90 degrees.

Part A

What is the torque τA about axis A due to the force F⃗ ?

Express the torque about axis A at Cartesian coordinates (0,0).

τA =

SubmitHintsMy AnswersGive UpReview Part

Part B

What is the torque τB about axis B due to the force F⃗ ? (B is the point at Cartesian coordinates (0,b), located a distance b from the origin along the y axis.)

Express the torque about axis B in terms of F, θ, ϕ, π, and/or other given coordinate data.

τB =

SubmitHintsMy AnswersGive UpReview Part

Part C

What is the torque τC about axis C due to F⃗ ? (C is the point at Cartesian coordinates (c,0), a distance c along the x axis.)

Express the torque about axis C in terms of F, θ, ϕ, π, and/or other given coordinate data.

τC =

SubmitHintsMy AnswersGive UpReview Part

Part D

What is the torque τD about axis D due to F⃗ ? (D is the point located at a distance d from the origin and making an angle ϕ with the x axis.)

Express the torque about axis D in terms of F, θ, ϕ, π, and/or other given coordinate data.

apricotclam488

Weekly leaderboard

Home

Homework Help 3,900,000

Physics 110,000

Related textbook solutions

Physics: Principles with Applications

Related questions

Weekly leaderboard