Consider a lamina occupying the region R and having the density function p. Use a computer algebra system (CAS) to answer the following questions. R is the triangular region with vertices (0, 0), (1, 1), and (0, 7); p(x, y) = x+y. (a) Find the moments M, and M, about the x-axis and y-axis, respectively. MX My-20.125 (b) Calculate the center of mass of the lamina. (x,y)- (c) Use a CAS to locate the center of mass on the graph of R. 5 6 5 5 5 4 0.2 04 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 O 0.2 0.4 0.6 0.8 1.0

Consider a lamina occupying the region R and having the density function p. Use a computer algebra system (CAS) to answer the following questions. R is the triangular region with vertices (0, 0), (1, 1), and (0, 7); p(x, y) = x+y. (a) Find the moments M, and M, about the x-axis and y-axis, respectively. MX My-20.125 (b) Calculate the center of mass of the lamina. (x,y)- (c) Use a CAS to locate the center of mass on the graph of R. 5 6 5 5 5 4 0.2 04 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 O 0.2 0.4 0.6 0.8 1.0

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.11P

See similar textbooks

Similar questions

Problem 1: For the vectors E = 2â – 4 ý+32. F = 38-j+52 then: 1. Find the tangential component E, of É (the component of E along F ). And also find the normal component É, of Ë that is normal on F. 2. Determine a unit vector perpendicular to both E and F. 3. The angle between the two vectors.
a. Prove the triple product identity Ax(B×C)= B(A·C)-C(A·B). Begin by adopting a Cartesian coordinate system. Without loss of generality, you may orient your coordinate system such that the x axis is along B, so that B = Bi. You then have the freedom to place the y axis in the plane defined by B and C. (But wait- what happens if B and C point in the same direction, so that no such plane is defined?) Very Strong Hint: I did this in class. Look in the book!
à ở từ if a = 2.8i+ 5.7 j – 8.1k, = b = − 4.9î + 4.4ĵ + 3.8k, and What are (a) the x component, (b) the y component, and (c) the z component of 7 1.8î + 2.8ĵ + 4.6k . (d) Calculate the angle between and the positive z axis. (e) What is the component of a along the direction of b? (f) What is the magnitude of the component of a perpendicular to the direction of b but in the plane of a and b? =
Ex. 3: A light thin uniform rod of 0.8 m length has two masses each of 16 gm stuck at its ends. Treating the masses neglecting the M.I. of the rod itself. Find the M.I. of the system about transverse axis through one end. as point masses and
Which are possible errors in Visual Python? Select one: O Syntax and Math (Logic) O Systematic and Math (Logic) O Syntax and Random O Random and Math (Logic) To define an angle of 25 degrees in radians using Visual Python, it is needed to be written: Select one: O 25/pi*180 O 25pi/180 25/pi/180 O 25*pi/180 Visual python display window coordinates are formed with (x.y.z) where y represents Select one: O in/out of the display window O None of the choices fits O horizontal axis O vertical axis
Consider two vectors Ã = (1, – 3,0) and B = (0 ,0,7). Let C be their cross product: Č = Ã × В. a) Calculate the Cartesian components of C. b) What is the angle between vectors B and C?
Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to solve the following problems. Determine the magnitude of the resultant R and the angle e between the x-axis and the line of action of the resultant for the following: 500 N 250 N 750 N
For Problem 9.13, how do I appropriately answer this?
Consider three vectors: What is the result of 2A (B-3C)? ) What is the result of A A+B B+ C. C? . . A = (9.71) 7+ (1.12)ĵ B = (7.28)i + (5.54)ĵ Č= (-2.95) + (-14.7)} - EU
1. a) Define a holonomic constraint and explain the impact of such constraints on the number of degrees of freedom of a system. Give an example of a non-holonomic constraint. b) Five identical flat circular plates are served on a circular conveyor belt. The plates have mass m, radius 5 cm and moment of inertia Ip about their axis of symmetry. They are free to move under gravity on top of a conveyor belt which has inner radius a, outer radius b and moment of inertia Ic about a vertical axis through its centre. From above, it looks like the diagram below. a The belt is banked at a fixed angle a such that the inner edge is lower than the outer edge. Assuming the conveyor belt rotates freely, how many degrees of freedom does this system have? Find the Lagrangian for the system. Hence find and identify any conserved quanti- ties of the system. 1 1
If the Lagrange's function is given by m (ỉ + 9192 + 92) – V(q1,92). L Prove that 2 (а) Н — Зт ;(Pỉ + p3 – Pip2) + V(91,92). 2 (b) Equation of motion is ĝ2 = əv av - 3m (aq2 ? Answer.
Assume = 36 and H = 4. Determine the x-component of H.