statics
Express the unit vectors \((i, j, k)\) in terms of unit
vectors \(\left(\underline{e}_{r}, \underline{e}_{\theta}, \underline{e}_{z}\right)\) (i.e. basis vector for cylindrical coordinates). Express the 1000 lb force going through the origin and through the point (2,4,4) in terms of the unit vectors \((i, j, k)\) and \(\left(e_{r}, e_{\theta}, e_{z}\right)\) with \(\theta=60^{\circ}\).
Homework Answers
Part B Express force FCa as a Cartesian vector Express your answer in terms of the...
Part B Express force FCa as a Cartesian vector Express your answer in terms of the unit vectors i,j. and k. Use the vec' button to denote vectors in your nswers. Express your significant figures. answer using three lb Submit Give Up Part C Express force FDA as a Cartesian vector Express your answer in terms of the unit vectors i,j. and k. Use the vec button to denote vectors in your answers. Express your answer using three significant figures....
A proton moves along the x-axis with v_x = 1.0 times 10^7 m/s. As it passes...
A proton moves along the x-axis with v_x = 1.0 times 10^7 m/s. As it passes the origin, what are the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position? Give your answer using unit vectors. Express your answer in terms of the unit vectors i, j, and k. Use the 'unit vector' button to denote unit vectors in your answer. B = T As it passes the origin, what are the strength...
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es ...
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es (x,y, z) by the transformat ion a) The line-element in Cartesian coordinates is given by d82-dr2+dy2+d22-De- termine the lne-elemen expressed in terms of the parabolic cylindrical coordinates b) Given F = 211,2) of the equation V22) F e where F depends only nu. Find the explicit form F-x F kF c) Solve the equation fro b) to find F Useful formulas: Given any ort...
A dog goes through a park. Its displacement is described by the following equations: x(t) =...
A dog goes through a park. Its displacement is described by the following equations: x(t) = 28.0 + 7.2t -0.31t 2 and y(t) = 30.0 -9.1t + 0.22t2 Positions and time are expressed in m and s, respectively. a) At t = 15 s, determine the position vector r of the dog in terms of unit vectors i and .k b) Determine for t = 15 s the velocity vector v of the dog terms of the unit vectors i...
HINT: this problem is about using different coordinate systems to solve kinematics problems! D 4. As...
HINT: this problem is about using different coordinate systems to solve kinematics problems! D 4. As rod OA rotates, pin P moves along the curve BCD with a constant speed of 3 m/s (in the counterclockwise direction). The equation for this curve is r = 2/(1+cose). Solve the following for the point shown, when 0 = 1/6 (radians). 0 1m B a) Find dr/dt and do/dt, and express the velocity vector in polar coordinates. b) Find the polar unit vectors...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
HOMEWORK 3 2.5-2.6 Problem 2.75 1 of 5 The spur gear is subjected to the two...
HOMEWORK 3 2.5-2.6 Problem 2.75 1 of 5 The spur gear is subjected to the two forces caused by contact with other gears.(Figure 1) Express Fi as a Cartesian vector Express your answer in terms of the unit vectors i, j, and k. F0,14.0,48.0 lb Submit Previous Answers Request Answer Figure X Incorrect; Try Again; 3 attempts remaining 1 of Part B 60P Express F2 as a Cartesian vector Express your answer in terms of the unit vectors i,j, and...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
Imagine acoordinates ystem Oxyz attached to amerry-go-rounddisk,with its origin Oat the disk centre, with the x-axis instantaneously going through 3 o’clock, the y-axis through 12 o’clock (both in t...
Imagine acoordinates ystem Oxyz attached to amerry-go-rounddisk,with its origin Oat the disk centre, with the x-axis instantaneously going through 3 o’clock, the y-axis through 12 o’clock (both in the horizontal plane of the rotating disk) and the z-axis vertically upwards. Unit vectors i, j, k, are along the x,y,z axes respectively. The merry- go-round is rotating at a constant rate of 0.5k rad/s. A person sitting on the disk located at 6 o’clock throws a ball horizontally towards 12 o’clock...
Part B Express force FCa as a Cartesian vector Express your answer in terms of the unit vectors i,j. and k. Use the vec' button to denote vectors in your nswers. Express your significant figures. answer using three lb Submit Give Up Part C Express force FDA as a Cartesian vector Express your answer in terms of the unit vectors i,j. and k. Use the vec button to denote vectors in your answers. Express your answer using three significant figures....
A proton moves along the x-axis with v_x = 1.0 times 10^7 m/s. As it passes the origin, what are the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position? Give your answer using unit vectors. Express your answer in terms of the unit vectors i, j, and k. Use the 'unit vector' button to denote unit vectors in your answer. B = T As it passes the origin, what are the strength...
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es (x,y, z) by the transformat ion a) The line-element in Cartesian coordinates is given by d82-dr2+dy2+d22-De- termine the lne-elemen expressed in terms of the parabolic cylindrical coordinates b) Given F = 211,2) of the equation V22) F e where F depends only nu. Find the explicit form F-x F kF c) Solve the equation fro b) to find F Useful formulas: Given any ort...
HINT: this problem is about using different coordinate systems to solve kinematics problems! D 4. As rod OA rotates, pin P moves along the curve BCD with a constant speed of 3 m/s (in the counterclockwise direction). The equation for this curve is r = 2/(1+cose). Solve the following for the point shown, when 0 = 1/6 (radians). 0 1m B a) Find dr/dt and do/dt, and express the velocity vector in polar coordinates. b) Find the polar unit vectors...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
HOMEWORK 3 2.5-2.6 Problem 2.75 1 of 5 The spur gear is subjected to the two forces caused by contact with other gears.(Figure 1) Express Fi as a Cartesian vector Express your answer in terms of the unit vectors i, j, and k. F0,14.0,48.0 lb Submit Previous Answers Request Answer Figure X Incorrect; Try Again; 3 attempts remaining 1 of Part B 60P Express F2 as a Cartesian vector Express your answer in terms of the unit vectors i,j, and...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
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