Find the mass and center of mass of the lamina that occupies the region D and has the given density function p. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); p(x, y) = 8(x + y) 48 m = (x, y) = 3 3 2 4

Find the centre of mass of the 2D shape bounded by the lines y = 10.9 between z = 0 to 2.9. Assume the density is uniform with the value: 2.9kg. m 2 Also find the centre of mass of the 3D volume created by rotating the same lines about the z-axis. The density is uniform with the value: 2.3kg. m-³ (Give all your answers rounded to 3 significant figures.) a) Enter the mass (kg) of the 2D plate: Enter the Moment (kg.m) of the 2D plate about the y-axis: Enter the z-coordinate (m) of the centre of mass of the 2D plate: b) Enter the mass (kg) of the 3D body: Enter the Moment (kg.m) of the 3D body about the y-axis: Enter the x-coordinate (m) of the centre of mass of the 3D body:

a particle with a mass of m1 slides down a frictionless road from point A to the stationary state. This particle hits another m2=3m1-mass stationary particle at point B. The observed orbit is horizontal at point B. a) Find the range of values that the collision coefficient e can take to move the m1 mass particle upwards (B to A) after impact. b) To e=0.5, find the h* height of the m1 mass particle and the w distance that the m2 mass will take horizontally.

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