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You’re a civil engineer for an advanced civilization on a solid spherical planet of uniform density. Running out of room for the expanding population, the government asks you to redesign your planet to give it more surface area. You recommend reshaping the planet, without adding any material or
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- A space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. P11.26 Ki+Ui=Kf+Uf12mvi2+GMEm(1rf1ri)=12mvf212vi2+GME(01RE)=12vf2orvf2=v122GMEREandvf=(v122GMERE)1/2,vf=[(2.00104)21.25108]1/2m/s=1.66104m/sarrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forwardZero, a hypothetical planet, has a mass of 4.7 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? (a) Number: i Units: (b) Number: i Units:arrow_forward
- Suppose we drill a hole through the Earth along its diameter and drop a small mass m down the hole. Assume that the Earth is not rotating and has a uniform density throughout its volume. The Earth’s mass is ME and its radius is RE. Let r be the distance from the falling object to the center of the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is moving inside the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is outside the Earth. On the graph below, plot the gravitational force on the small mass as a function of its distance r from the center of the Earth. Determine the work done by the gravitational force on the mass as it moves from the surface to the center. What is the speed of the mass at the center of the Earth if the Earth has a given density Determine the time it takes the mass to move from the surface to the center of the Earth.arrow_forwardA spherical shell has uniform density of 4.6 kg/m³. It has an inner radius 2.5 m and outer radius 4.2 m. The magnitude of the gravitational force exerted on the shell by a point mass particle of mass 9.5 kg a distance 2.1 m from the center, is 6.5 x 10 ⁹ N 24 x 10 N 3.2 x 10¹ N O 1.1 x 10 N ONarrow_forwardAround 2.5 centuries ago, several physicists of the time came up with the notion of a dark star. This was a star so dense, with so much gravity, that not even light could escape. The calculations used Newtonian mechanics. In class, we calculated the escape speed from the surface of the earth or the distance from the sun, and the mass of the planet or star. Here, the process is partially reversed. Calculate the dark star radius from the mass of the star and the escape speed. Answer in kilometers. c = 3*108 m/s M = 2.4*1030 kg G = 2/3 * 10-10 N*m2/kg2arrow_forward
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- A 19 kg. rock is thrown straight down toward the Earth from a distance of 10 earth radii above the surface of the Earth with a speed of 5400 m/s. The radius of the Earth is 6370000 meters. The mass of the earth is 5.98e+24 kg. (A)Find the initial kinetic energy of the rock (in J) (B)Find the initial potential energy (in J) of the rock (HINT: the "r" in the potential energy formula is measured from the CENTER of the Earth). (C)Find the total initial energy (in J) of the rock (D)What is the potential energy (in J) of the rock after it has fallen 4 Earth radii from its original position. (E)Using the Conservation of Energy, find the speed (in m/s) of the rock after it has fallen 4 Earth radii from its original position.arrow_forwardA planet has a mass of 4.0 × 1024 kg and a radius of R = 5.0 × 106 m. A cannon on the planet's surface launches a projectile directly away from the planet's surface so that it reaches a distance of 1.5 × 107 m from the planet's center. At what speed was the projectile launched? Group of answer choices 1.0 × 104 m/s 6.0 × 103 m/s 4.9 × 103 m/s 8.4 × 103 m/s 1.5 × 104 m/sarrow_forwardhi. can you solve it with an explanation? thanksarrow_forward
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