A system of three particles with masses m₁ = 5m at position (0, 0, -d), m2 = 7m at position (d, 0, d),1507and m3 = 3m at position (0, d, 0) has an inertia tensor of I = md²0190about the origin.7010What are the principal moments of inertia of the system?Enter the moments of inertia from smallest to largest.First moment = Ex: 1.23Second moment = Ex: 1.23Imd²Third moment = Ex: 1.23md²md²

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Answered: A system of three particles with masses…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(4) A particle moves from point (1,2,3) to point (3,5,2) under the action of force F₁ = 2 i + j + 3k and F₂ = 31-4j-2k. Find the work done by the force.
Find the position r(t) acceleration a(t) = (3 cos t, 2 sin t, 2)- v(0) = (0,0, 1) of a particle that begins at r(0) = (2, 1,0) and has and initial velocity Select one: a. r(t) = (5+ 4t - 3 cos t, 1-t-2 sin t, t2 + 2t) b. r(t) = (5 – 3 cos t, 1 + 2t- 2 sin t, t2 + t) C. r(t) = (5 +2t – 3 cos t, 1 +3t - 2 sin t, t² +t+ 1) d. r(t) = (4+t-3 cos t, 2+ 3t – 2 sin t, t2) e. r(t) = (5 -t- 3 cos t, 1 +t-2 sin t, t2)
3) Obtain the Position, Velocity and Acceleration Vectors of the particle whose behavior is described with the vector function with respect to time. (t) = 6t² i +2j + 4t k p= 7 = à = t = 3
Two blocks of masses m1 and m2 (m1 > m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude f is applied to the block of mass m1 in Figure P4.32. (a) If P is the magnitude of the contact force between the blocks, draw the free-body diagrams for each block. (b) What is the net force on the system consisting of both blocks? (c) What is the net force acting on m1? (d) What is the net force acting on m2? (e) Write the x -component of Newton’s second law for each block. (f) Solve the resulting system of two equations and two unknowns, expressing the acceleration a and contact force P in terms of the masses and force. (g) How would the answers change if the force had been applied to m2 instead? (Hint: use symmetry; don’t calculate!) Is the contact force larger, smaller, or the same in this case? Why?
Car A rounds a curve of radius p = 230 m at a constant speed of 18 m/s. At the instant represented, car B is moving at 23 m/s but is slowing down at the rate of 4 m/s². Determine the vectors of the velocity and acceleration of car A as observed from car B. (ÑA/B = −23î + 18ĵ m/s, āa/B m/s²) = = 2.591 ρ y B A x
Find an initial point P of a nonzero vector m = P& with ter-minal point O(3. 0. -5) and such that(a) u has the same direction as v = (4, -2, -1).
9. A vertical tower AO of height h metres stands with its base A on horizontal ground. A stone is projected horizontally from the top O of the tower with speed V ms ¹. The stone moves in a vertical plane under gravity where the acceleration due to gravity is g ms 2. At time t seconds its position vector relative to O is r(t) = Vt i-lgt² j The stone hits the ground at an angle of 45° to the horizontal. What is the time of impact? (A) (B) (C) (D) V 2g V g 2V g 4V g seconds seconds seconds seconds
B/ show that if u(t) = à cos t + b sin t, where a and b* are constant vectors |du d'u dt then ü(t). = 0 كلية العلوم بالفرعية
The position vector of a particle is r(t). Find the requested vector. 5) The acceleration at t = for r(t) = (4 sin 41)i - (10 cos 41)j + (5 csc 41)k 5) A) = -64i + 80k B) a = -64i - 80k 8 = 64i + 80k 160j + 80k

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