Three small but dense objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA = 3.25 kg, mB = 2.01 kg and mc = 1.65 kg. = y (m) 9 8 7 сл 3 2 1 0 1 2 3 5 6 7 B 8 9 4 x (m) Determine the x and the y coordinates of the center of the mass of this system. All three objects are small in size, they can be treated as point masses. x coordinate: y coordinate:
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- The figures show a hypothetical planetary system at two different times. The system has a star S and three planets, labeled A, B, and C. The table provides the mass of each body in the system, as well as their spatial coordinates (x, y) in their initial and final positions. The spatial coordinates of the bodies are given in Astronomical Units (AU). Initital Position Body S A B с Mass (kg) mg = 2.3863 × 10³⁰ mA = 2.1957 × 1028 mB = 6.2841 × 1026 mc = 7.8063 × 1027 The initial velocity of the center of mass of the system is zero. Find the magnitude ds of the star's displacement from the origin in its final position. C S (0,0) (0,0) (0.4815, 0) (0.4373, 1.3397) (0, 1.6711) A Final Position (xs, ys) (0, -0.4913) B (-1.6007, 0) (-0.8443,-0.7481) B ● С. S AThe spherical shell has a uniform mass density of ρmass=20.0kg/m3= with the shell radius extending from r = 3.6 to 8.1 cm. Find the total mass of the spherical shell. If half the total mass is located in the region 3.6 cm < r < r1 , find r1 (in cm). Use at least 3 significant figuresTwo masses are given. Let's say we have a M1 and M2. Let's just say. Let's examine this hypothetical situation. The first mass would be 1.50 kg and the second mass would be 2.00 kg. These two masses would then be separated by a length or we should say a distance of this L = 2.50 m. Let's say we want to place a third mass (immaterial mass) in the middle of the two masses, such that there would be no net force. Find this specific place where this would occur, and to make it easy, find the distance from the first mass towards this third mass
- The center of a moon of mass m = 8 × 1023 kg is a distance D = 97 × 105 km from the center of a planet of mass M = 10.9 × 1025 kg. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero. a. Derive an expression for x. b. Calculate x in kilometers, given the variables in the beginning of the problem.Sally and Sam are in a spaceship that comes to within 13,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 1020 kg and the mass of Sally is 74 kg. For calculation purposes, assume the two objects to be point masses. N?One type of engine used in space travel is an ion thruster. These engines produce a low force that results in small acceleration changes. If an ion-thrust engine is used to apply 87 millinewtons [mN] of force on a satellite with a mass of 1.7 megagrams [Mg], what is the acceleration produced in units of meters per second squared [m/s2]?
- Question 2: An OSU-branded squishy moon ball has a mass of 25 g and a diameter of 60 mm. Consider two squishy moons located in deep space far from the Sun or any other massive body. The two squishy moons form a binary system with their centers separated by 0.5 meters, and they are in circular orbits around their common center of mass. a. Draw a sketch of the squishy moon system and correctly label the dimensions and orbits. b. What is the orbital period of the two squishy moons about their center of mass? c. What is their orbital speed? d. If the squishy moon binary system is 5au from the Sun, what is the Hill radius of the system in the tidal field of the Sun? Compare the Hill radius to the semi-major axis of the squishy moon binary orbit radius and comment on whether this binary squishy moon system is stable when it is 5au from the Sun. e. Follow-up your answer to part d and estimate the distance from the Sun where the squishy moons in this binary system are exactly twice their Hill…Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]ll Problem Three. Consider two planets: Neptune with a mass of m, × 1.02×10% kg and Uranus with a mass of m, = 8.68 x10*kg. The planets are a distance of d =1.62×10°km apart. Let Neptune be at the origin of a coordinate system, and Uranus be along the positive x-axis. (See the diagram below.) m2 X Find the location "x" where a test particle would accelerate toward the two planets with a force that is half due to Neptune, and half due to Uranus. Give an answer in 1010 km. 7.) (A) 5.6 B) 3.6 (C) 9.4 (D) 2.1 (E) 8.9 Consider if a large asteroid of mass m =1.00×10²ºkg is a distance d above m. Find the magnitude of the gravitational force the asteroid experiences due to both planets. Give an answer in units of 1010 N. 8.) (A) 35 (B) 83 (C) 71 (D) 53 (E) 98
- Constants Every few hundred years most of the planets line up on the same side of the Sun. Part A Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line,(Figure 1). The masses are my — 0.815mE, тj — mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km. 318mв, mSat %3D 95.1mв, and the Figure 1 of 1 Express your answer to three significant figures and include the appropriate units.You have been assigned to a team charged with developing a plan to explore a new planetary body called Planet Z. The acceleration due to gravity of Planet Z is 2.8 meters per second squared [m/s]. A container of unknown volume is filled with cooking oil, with a specific gravity = 0.93, on Planet Z where the liquid in the container weighs 4 pound-force [Ib;]. What is the volume of cooking oil in the container in units of liters [L]? E Click the icon to view the table of common derived units in the SI system. E Click the icon to view the conversion table. The volume is L. (Round your answer to two decimal places.)Migrating land mammals are often called runners because of the large distances that they can cover in one day. The velocity (speed) of a migrating land mammal or runner in relation to its mass can be modeled by the equation V(m) = 9.31m0.12, where m is the mass of the animal in kilograms and V is the velocity in kilometers per day. Round your answers to the tenths place, if necessary. Part A: Complete the table by determining the velocity of several different runners. Animal Mass (kg) Velocity (km/day) Grey Wolf 40 14.494 OB Zebra American Buffalo African Elephant 270 900 5000 Answer: It will travel 1 18.227 Part B: How does the mass of the elephant compare to the mass of the zebra? How do their velocities compare? 21.062 X Answer: The mass of the elephant is 18.51 elephant is 1.419 x times that of the zebra. Answer: Answer: The mass of the buffalo is 22.5 1.5 ✓o times that of the wolf. OB 25.872✓ O Part C: How does the mass of the buffalo compare to the mass of the wolf? How do their…