1. [-/2 Points] DETAILS SERPSE10 9.6.OP.024. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The mass of Mercury is 3.30 x 1023 kg, and the mass of Earth is 5.97 x 1024 kg. The average distance of separation, measured between their centers, is 9.13 x 107 km. (a) Locate the center of mass (in m) of the Mercury-Earth system as measured from the center of Mercury. m from Mercury's center (b) Is the center of mass of the system located within Mercury? (Assume Mercury has a radius of 2.44 x 106 m.) Yes No Need Help? Read It 2. [-/1 Points] DETAILS SERPSE10 9.6.P.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown in the figure below. The monument is made from tens of thousands of small stone blocks of density 2 528 kg/m. The monument is 14.6 m high and 64.6 m wide at its base and is everywhere 2.70 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. 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 U = Mgy CM, where M is the total mass of the object and YCM is the elevation of its center of mass above the chosen reference level. g 3. [-/2 Points] DETAILS SERPSE10 9.6.P.024. A uniform piece of sheet metal is shaped as shown in the figure below. Compute the x and y coordinates of the center of mass of the piece. x = y = y (cm) cm cm 30 20 10 x (cm) 10 20 30 Need Help? Read It Watch It 4. [-/2 Points] DETAILS SERPSE10 9.6.P.026. A rod of length 20.50 cm has linear density (mass per length) given by = 50.0 + 24.0x where x is the distance from one end, and 2 is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass? m Need Help? Read It MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 5. [-/2 Points] DETAILS SERPSE10 9.6.OP.026. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the schematic of the molecule shown, with two hydrogen atoms, H, bonded to an oxygen atom, O. The angle between the two bonds is 106. If the bond length r = 0.102 nm long, locate the center of mass of the molecule. The mass m of the hydrogen atom is 1.008 u, and the mass mo of the oxygen atom is 15.9999 u. (Use a coordinate system centered in the oxygen atom, with the x-axis to the right and the y-axis upward. Give the coordinates of the center of mass in nm.) XCM H 53 53 nm nm H 6. [-/2 Points] DETAILS SERPSE10 12.2.P.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A carpenter's square has the shape of an L as shown in the figure below. Locate its center of gravity. (Take (x, y) = (0, 0) at the intersection of d and d. Assume d = 21.0 cm, d = 3.00 cm, d3 = 3.00 cm, and d4 11.0 cm.) L d Need Help? d4 d3 cm Read It Watch It 7. [-/2 Points] DETAILS SERPSE10 12.2.OP.002.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following distribution of objects: a 1.00-kg object with its center of gravity at (0, 0) m, a 5.20-kg object at (0, 3.00) m, and a 3.40-kg object at (5.00, 0) m. Where should a fourth object of mass 9.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0, 0)? m Need Help? Read It Master It 8. [-/1 Points] DETAILS SERPSE10 12.2.P.004. MY NOTES ASK YOUR TEACHER A circular pizza of radius R has a circular piece of radius R/2 removed from one side as shown in the figure below. The center of gravity has moved from C to C' along the x axis. Show that the distance from C to C' is R/6. Assume the thickness and density of the pizza are uniform throughout. C i