In a hydrochloric acid (HCI) molecule, the distance between the hydrogen atom and the chlorine atom is 1.27 x 10 10 meters. The mass of an hydrogen atom is 2 atomic mass units (amu) and the mass of a chlorine atom is 35 amu. How far from the hydrogen (H) atom is the center of mass of the molecule, in meters? Justify your answer using your equations and rationale used.
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- In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 × 10–11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L = 10.14 × 10–11 m. What are the (a) x and (b) y coordinates of the molecule's center of mass?A certain carbon monoxide molecule consists of a carbon atom of mass mc = 14 u and an oxygen atom of mass mo = 18 u that are separated by a distance of d = 122 pm, where "u" is an atomic unit of mass. a. Write a symbolic equation for the location of the center of mass of the carbon monoxide molecule relative to the position of the oxygen atom. This expression should be in terms of the masses of the atoms and the distance between them. b. Calculate the numeric value for the center of mass of carbon monoxide in units of pm.Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object–Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.
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- The figure below shows four objects at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the objects are: m1 = 2.90 kg, m2 = 1.90 kg, m3 = 4.10 kg, m4 = 2.50 kg. a) What is the moment of inertia (in kg · m2) of the system about the x-axis? ____ kg · m2 (b) What is the moment of inertia (in kg · m2) of the system about the y-axis? _____kg · m2 (c) What is the moment of inertia (in kg · m2) of the system about an axis through O and perpendicular to the page (that is, the z-axis)? _____kg · m2A thin rod of length 2.6 meters has a non-uniform density given by ρρ = b(x2 + ax) where b = 1.18 kg/m3, a = 0.32 m, and x measures from one of the rod to the other. Find the rod's center of mass.The four masses shown in the diagram are connected by massless, rigid rods. The mass of the A particle is 400 g, the mass of the B particle is 900 g, the mass of the C particle is 500 g, and the mass of the D particle is 450 g. The length of the rods is 10 cm. Consider the A particle to be the origin of the coordinate system. The x coordinate of the center of mass (in cm) is? Consider the A particle to be the origin of the coordinate system. The y coordinate of the center of mass (in cm) is ? Find the moment of inertia (in kg*m*m) about an axis that passes through mass A and is perpendicular to the page.