A uniform square of mass 4 kg and sides 2 m and negligible thickness is centered at the origin. Determine the center of mass of this square using symmetry arguments. Suppose then that the 1 m × 1 m section in the fourth quadrant is removed. Where is the center of mass of this new object? Do this calculation by treating the mass of each remaining 1 m × 1 m section as residing at its center of mass and then fnding the centers of mass of these “masses”.

Find the center of mass of a rod of length L whose mass density changes from one end to the other quadratically. That is, if the rod is laid out along the x-axis with one end at the origin and the of end at x = L, the density is given by p(x) = Po + (P, - PoE where Po and e, are constant values. (Use the following as necessary: L, Po, and e,.) XCM =

Center of a mass

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

Calculate the center of mass of the upper-arm and forearm of a 75 kg athlete using the appropriate anthropometric tables, when we know the position of Marker1 is (3.5,4.5), Marker 2 is (5,3), and Marker3 is (7,4). The upper arm is defined by markers Marker1 to Marker2, whereas the forearm is defined by markers Marke2 to Marker3.

Find the center of mass coordinates XCM y YCM of the arrangement of masses shown. Assume that the connecting bars are massless. (m= 3.0 kg; M = 1.5 kg; L = 2.0 m)

A child in a boat throws a 5.50-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 26.6 kg and the mass of the boat is 36.4 kg. Calculate the velocity of the boat immediately after, assuming it was initially at rest.Express your answer to three significant figures and include the appropriate units. Enter positive value if the direction of the velocity is in the direction of the velocity of the box and negative value if the direction of the velocity is in the direction opposite to the velocity of the box.

A game of billiards is being played with ball that are spherical shells of mass M and radiusR. Where should the ball contact the sharp edge of the bumper in order for there to be noreaction force of the ball on the felt?

Three point masses ( 2 kg. 2 kg. 6 kg) shown in the figure are initially at rest on a frictionless horizontal floor. When the mass at the origin is subjected to a constant force F, it is observed that the center of mass (CM) of the three-mass system reaches point P with coordinates (4 m, 4 m) in 2 sec. Find the acceleration of the center of mass in unit vector notation. (Hint: after finding center of mass location, need to use kinematics) 2kg Y (m) 1X 4 2kg 4 メ (m)

Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is 3 kg.