Question 9: A half uniform annulus of inner and outer radii R1 and R2 has a non- uniform surface mass density given by o = 0or where oo is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 6. Find i) the mass of the half annulus, and ii) the position of the center of mass, i.e., (xem, Yem) the center of mass in terms of Rị and R2. R2 M R Figure 6

Question 9: A half uniform annulus of inner and outer radii R1 and R2 has a non- uniform surface mass density given by o = 0or where oo is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 6. Find i) the mass of the half annulus, and ii) the position of the center of mass, i.e., (xem, Yem) the center of mass in terms of Rị and R2. R2 M R Figure 6

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Momentum And Collisions

Section: Chapter Questions

Problem 38P

See similar textbooks

Similar questions

Find the total mass of a mass distribution of density o in a region T in space. o = e*-)-<,T the tetrahedron with vertices (0,0, 0), (2,0, 0), (0, 2,0), (0, 0, 2) -x-y-z Round your answer to 2 decimal places. odxdydz = i T
A stationary nucleus decays into 3 particles. Determine the sum of the momentum vectors after the decay. Be specific.
Sulfur dioxide 1SO22 consistsof two oxygen atoms (each of mass 16 u, where u is defined inProblem 39) and a single sulfur atom (of mass 32 u). The centerto-center distance between the sulfur atom and either of the oxygen atoms is 0.143 nm, and the angle formed by the three atoms is120°, Find the x and y coordinates of thecenter of mass of this molecule.
A rod of length 3 meters with density 8(x) = 1.1 + 1.1x4grams/meter is positioned along the positive x-axis, with its left end at the origin. Find the total mass and the center of mass of the rod. Round your answers to four decimal places. The total mass of the rod is i The center of mass of the rod is i grams. meters.
3 kg and m, = 1 kg move in the directions shown in Figure. Before the and m, has an initial velocity of 5 m/s. After the collision, the half of kinetic energy is lost. Find the velocities of the masses m, and 3) The masses m, = %3D collision, the momentum of m, is equal to the momentum of m, m, after the collision. (sin53=0.8 cos53=0.6)
A square plate is points (0,0), (0,1), (,0) and density plx,y)= =xy. Find the mo ss of the plate and the center of mass with vertices the engiven
You are handed a bat that is 6 times as dense on one side as it is on the other side, and 3 times as dense in the middle as it is on the least dense side. Density varies quadratically. The mass of the bat is M and the length is L. Write your answers only in terms of these constants. Calculate center of mass using integral
Problem 3 A hollow sphere of mass m and radius R has its center of mass at rest as it spins at a given wo. Two point masses, each of mass m, travel with exactly opposite velocities and collide simultaneously at mirror image angles as drawn. Given the angle a, find an expression for the angle between the spin vectors just before and just after the collision. Two ma before rĵ 'm m after
u suodaling A fariticle of mass (m) įi in a plane in civeculae peith of ecadiu c). 9t3 angeulay momenlim is CA). The cerbipetal fouce acling on pavilicle és ?
How do you find the the center of mass of a lamina whose density is given by p(x, y) on a region R?? Here m is the mass, M, is the moment in the x- axis and My is the moment in the y- axis М, М, Center of mass is located at т m The coordinates of the center are (M2, My) Find the moment M, and divide by the mass m The center of mass is located in the center of the universe. Find the moment M, and divide by moment My о ООО
Problem 1 Not So Simultaneous = The positions of two masses, ma and mb, are described by the equations: a(t) 3A sin (4wt) and xb (t) = 2A sin (3wt). (a) Not including t = 0, what are the first three times that the masses will pass through their respective equilibrium positions simultaneously? (b) Find the two expressions that would describe each mass' velocity. What were the velocities at the times you found in part a?
Figure 2 shows a ballistic pendulum consists of 5 kg slender rod and 10 kg solid cylinder. The pendulum is originally at rest, θ = 0ᵒ. A 10 g bullet with velocity v is fired to the solid cylinder.a) Determine the location of ?̅ of the center of mass G of the pendulum. Then, calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G.b) Initially, it is estimated that the value of v is 622 m/s. Analyze the angular velocity of the cylinder just after the bullet embedded. Also, determine the expected value of maximum angle θ will swing when the pendulum stops. Then, evaluate the expected amount of energy lost during impact in percentage.c) However, it is observed that the cylinder swing upward to a maximum angle of θ = 22ᵒ. Determine the actual initial value of v. Then, analyze the linear impulse imparted by the bullet on the cylinder. Also, evaluate the force on the rod immediately just after the impact.