Find the mass and center of mass of the solid E with the given density function p. m (x, y, z) E is the tetrahedron bounded by the planes x = 0, y = 0, z = 0, x + y + z = 4; p(x, y, z) = 7y 224 3 8 16 8 5' 5' 5 cr100 ܗ
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- 9c Qa О qb a/2 30 30 2 a/2 a R 90 a 90 a/2 a/2 6060 R R 30 r 30 30 90 90 30 a/2 a/2 a http://www.treenshop.com/Ireenshop/ArticlesPages/HiguresUninterest Article/The%20Equilateral%20 Triangle.htm qa = +1.8 nc, qb = -7.5 nC, qc = -8.7 nC, a = 30.0 cm The point charges are located at the corners of an equilateral triangle of side a. Determine the electric field at the center of the right side of the triangle. R || = r = 3 h 6 tA water molecule consists of an oxygen atom and two hydrogen atoms. The two O—H bonds are each0.1 nm long and form an angle of 107◦ with each other. Where is the molecule’s centre of mass located?Consider the mass of the oxygen atom to be 16 times the mass of a hydrogen atom, and place yourhydrogen atoms along the x-axis of your coordinate system. [Hint: Draw your coordinate system!].Problem 9: A baseball of mass mj = 0.39 kg is thrown at another ball hanging from the ceiling by a length of string L = 1.35 m. The second ball m2 = 0.79 kg is initially at rest while the baseball has an initial horizontal velocity of V, = 3.5 m/s. After the collision the first baseball falls straight down (no horizontal velocity). Randomized Variables V, m1 = 0.39 kg m2 = 0.79 kg L= 1.35 m V1 = 3.5 m/s m, m,
- 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? =You're rolling solid rubber balls on the kitchen floor. Ball 1 has a density of 1.16 × 103 kg/m3 and a radius of 28.0 mm. Ball 2 has an unknown density and a radius of 43.0 mm and is initially at rest. You roll ball 1 at an initial speed of 3.00 m/s, and the two balls collide head-on. Ball 1 reverses direction and comes back to you at 2.00 m/s, and after the collision, the speed of ball 2 is 1.00 m/s. The positive x axis is in the direction of ball 1's initial motion. A.What is the magnitude of the initial momentum of ball 1? Express your answer with the appropriate units. B. What is the magnitude of the final momentum of ball 1? Express your answer with the appropriate units. C. What is the magnitude of the initial momentum of ball 2? Express your answer with the appropriate units.let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 8.61 kg, with x coordinate at 3.063 m and y coordinate at 3.826 m. The second atom has a mass of 63.048 kg, with x coordinate at 87.738 m and y coordinate at 51.326 m. The third atom has a mass of 26.317 kg, with x coordinate at 42.334 m and y coordinate at 23.115 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?
- A water molecule consists of an oxygen atomwith two hydrogen atoms bound to it. Theangle between the two bonds is 106◦. If each bond is 0.093 nm long, how far fromthe oxygen atom is the center of mass of themolecule? Take the mass of an oxygen atomto be 16 times the mass of a hydrogen atom.Answer in units of nmLet's consider the three atoms composing the molecule now have different masses and coordinate, while the axis of rotation is still y axis. The first atom has a mass of 9.199 kg, with x coordinate at 3.655 m and y coordinate at 8.442 m. The second atom has a mass of 41.619 kg, with x coordinate at 76.902 m and y coordinate at 57.706 m. The third atom has a mass of 39.818 kg, with x coordinate at 39.495 m and y coordinate at 25.9 m. What is the moment of inertia in unit of kg m2 with respect to the y axis?Problem 11: A merry-go-round at an amusement park consists of an outer ring of horses and an inner ring of elephants. The ring of eight horses has a radius of r = 8.1 m. Each of the eight horses has a mass m, = 95 kg. The ring of four elephants has a radius of r. = 6.4 m and each of the four elephants has a mass m. = 190 kg. The platform of the merry-go-round itself has a mass of m, = 1600 kg and a radius of r, = 10.7 m. At it's operating speed, the merry-go-round makes one revolution every t= 11 s.