(a) Calculate the work (in MJ) necessary to bring a 104 kg object to a height of 991 km above the surface of the Earth. -854 X The work done must provide the increase in gravitational potential energy, so calculate AU, for the system. You will need the radius and mass of the Earth for your calculation. MJ (b) Calculate the extra work (in J) needed to launch the object into circular orbit at this height. 2.619E9 Notice that the centripetal force for the object in orbit is due to the gravitational force from the Earth. Write and equate two expressions for the force, in terms of Newton's universal law of gravitation and the centripetal force, and solve for v2. The additional work is equal to the kinetic energy, so find K using your value for v². J

(a) Calculate the work (in MJ) necessary to bring a 104 kg object to a height of 991 km above the surface of the Earth. -854 X The work done must provide the increase in gravitational potential energy, so calculate AU, for the system. You will need the radius and mass of the Earth for your calculation. MJ (b) Calculate the extra work (in J) needed to launch the object into circular orbit at this height. 2.619E9 Notice that the centripetal force for the object in orbit is due to the gravitational force from the Earth. Write and equate two expressions for the force, in terms of Newton's universal law of gravitation and the centripetal force, and solve for v2. The additional work is equal to the kinetic energy, so find K using your value for v². J

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

**Problem Description:**

*(a)* Calculate the work (in MJ) necessary to bring a 104 kg object to a height of 991 km above the surface of the Earth.

- **Incorrect Answer Provided:** -854 MJ
- **Feedback:** The work done must provide the increase in gravitational potential energy, so calculate \( \Delta U_g \) for the system. You will need the radius and mass of the Earth for your calculation.

*(b)* Calculate the extra work (in J) needed to launch the object into circular orbit at this height.

- **Incorrect Answer Provided:** 2.619E9 J
- **Feedback:** Notice that the centripetal force for the object in orbit is due to the gravitational force from the Earth. Write and equate two expressions for the force, in terms of Newton's universal law of gravitation and the centripetal force, and solve for \( v^2 \). The additional work is equal to the kinetic energy, so find \( K \) using your value for \( v^2 \).

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