Find the center of mass of a quarter of a spherical shell of radius "a" shown in the figure.
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- (COLLAB) A new design of Saturn 10 rocket with mass 1.36 x10° kg has a propulsion engine that can eject gases at a constant speed of 324.31 m/s (vGas) by burning fuel at a rate of 3.23 x10 fuel of mass 41.42 x10 ° kg. If this design exceeds the velocity of 11,200 m/s it can can successfully escape Earth's gravity. Determine if this is so. Find its maximum velocity (velyZ). (Pitch Anglat = 0) kg/s (dmdT). In full tank, the rocket can carry aThree masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. Thedistance of the centre of mass from the origin is -(1) 45 cm (2) 50 cm (3) 30 cm (4) 40 cm5
- Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1050 kg and was approaching at 4.00 m/s due south. The second car has a mass of 900 kg and was approaching at 22.0 m/s due west. (a) Calculate the final velocity (magnitude in m/s and direction in degrees counterclockwise from the west) of the cars. (Note that since both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects.) magnitude m/s direction ° counterclockwise from west (b) How much kinetic energy (in J) is lost in the collision? (This energy goes into deformation of the cars.)The coordinates of the centre of mass of objects of mass 10, 20, 30 kg are (1,1,1) m. Where should an object of mass 40 kg be placed such that the centre of mass of this new system lies at (0,0,0)? a) 3/2, 3/2, 3/2 b) -3/2, -3/2, -3/2 c) 3/4, 3/4, 3/4 d) -3/4, -3/4, -3/4(2) Find the center of mass of the quadrant, a spherical shell of radius "a" shown in the figure.
- Three particles are located on the X-axis. A particle of mass 20 g is located at 0 m. A second particle of mass 20 g is located at 1 m. Where should a particle of mass 26 g be placed so that the Center of Mass of this system is at x=0? (Round your answer to one decimal and enter the units)Find the x center of mass of the following masses at their respective coordinates: m1=2.5, x1=0.6,y1=-0.6 m2=3.5, x2=2.8,y2=3.8 m3=4.0, x3=-2.4,y3=-2.6 x_com=?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) = x +y
- 11.Water droplets, of mass m in each, are dripping from height h at a rate of r per second. Find the center of mass of the droplets.Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1000 kg and was approaching at 4.00 m/s due south. The second car has a mass of 900 kg and was approaching at 15.0 m/s due west. (a) Calculate the final velocity (magnitude in m/s and direction in degrees counterclockwise from the west) of the cars. (Note that since both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects.) magnitude direction m/s • counterclockwise from west (b) How much kinetic energy (in J) is lost in the collision? (This energy goes into deformation of the cars.) ×