An astronaut working on the Moon tries to determine the gravitational constant G by throwing a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the Moon has a density pof 3340 kg/m and a radius Rof 1740 km. (a) Show with (1) that the potential energy of the rock at height h above the surface is given by: R 47G mp. 3 E (2) R+h (b) Next, show that the gravitational constant can be determined by: -1 3 v2 G 8n pR? R (3) R+h (c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?

An astronaut working on the Moon tries to determine the gravitational constant G by throwing a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the Moon has a density pof 3340 kg/m and a radius Rof 1740 km. (a) Show with (1) that the potential energy of the rock at height h above the surface is given by: R 47G mp. 3 E (2) R+h (b) Next, show that the gravitational constant can be determined by: -1 3 v2 G 8n pR? R (3) R+h (c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 52P

See similar textbooks

Similar questions

Find the escape speed of a projectile from the surface of Jupiter.
A system consists of five particles. How many terms appear in the expression for the total gravitational potential energy of the system? (a) 4 (b) 5 (c) 10 (d) 20 (e) 25
Find the escape speed of a projectile from the surface of Mars.
On the surface of the earth, the gravitational field (with z as vertical coordinate measured in meters) is F =〈0, 0, −g〉.(a) Find a potential function for F. (b) Beginning at rest, a ball of mass m = 2 kg moves under the influence of gravity (without friction) along a path from P = (3, 2, 400) to Q = (−21, 40, 50). Find the ball’s velocity when it reaches Q.
Calculate the total potential energy, in Btu, of an object with a mass of 200 lbm when it is 10 ft above a datum level at a location where standard gravitational acceleration exists.
A satellite from the Glonass navigation system weighs 7,350 N on the surface of Earth. How much work is donein propelling the satellite from the surface of the Earth to a medium Earth orbit (MEO) of 19,000 km above Earth’ssurface? Use 6,371 km as the radius of Earth. (Express the result with unit N·km rounded to the nearest integer.)
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ? = 2.67 × 106 g/m3 and volume V =1.71 × 1012 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 (Nm2)/(kg2).
A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What ratio m/M gives the least gravitational potential energy for the system?
A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg. A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei. B) Can it escape Jupiter? Justify your answer. C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.
There exista a spherical planet with a mass of M and a radius of R. How much energy is required to take a rocket of a mass m from rest on the surface of the planet to a circular orbit a height h above the surface?Find using the Energy Difference Ef -Ei where Ef is the energy in orbit and Ei is the energy at rest on the surface. h is not small
Show that the gravitational potential energy of an object of mass at height on Earth is given by PEg = mgh.
Assuming that the object are on Earth, where acceleration due to gravity is 10N/kg, calculate the gravitational potential energy that they had.