Question

Predict/Calculate REFERRING TO EXAMPLE $12-17$ Suppose the Earth is suddenly shrunk to half its present radius without losing any of its mass.(a) Would the escape speed of a rocket increase, decrease, or stay the same? (b) Find the escape speed for an Earth with half its present radius.

Name: Problem 98, Chapter 12: Physics
Uploaded: 2020-04-05T00:33:19-08:00
Duration: 2 min 19 s
Channel: Andy Chen
Description: Predict/Calculate REFERRING TO EXAMPLE 12-17 Suppose the Earth is suddenly shrunk to half its present radius without losing any of its mass.(a) Would the escape speed of a rocket increase, decrease, or stay the same? (b) Find the escape speed for an Earth with half its present radius.

   Predict/Calculate REFERRING TO EXAMPLE $12-17$ Suppose the Earth is suddenly shrunk to half its present radius without losing any of its mass.(a) Would the escape speed of a rocket increase, decrease, or stay the same? (b) Find the escape speed for an Earth with half its present radius.

Physics

James S. Walker 5th Edition

Chapter 12, Problem 98

Instant Answer

Solved by Expert Andy Chen

04/05/2020

Step 1

We can use the conservation of energy equation for this. The energy at the surface (position 1) is equal to the energy at infinity (position 2). The energy at the surface consists of kinetic energy and gravitational potential energy. At infinity, both kinetic and Show more…

Show all steps

Thanks for your feedback!

Predict/Calculate REFERRING TO EXAMPLE $12-17$ Suppose the Earth is suddenly shrunk to half its present radius without losing any of its mass.(a) Would the escape speed of a rocket increase, decrease, or stay the same? (b) Find the escape speed for an Earth with half its present radius.

Play audio

Feedback

Andy Chen and 54 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Escape Velocity

Escape velocity is the minimum speed that an object must reach to overcome the gravitational pull of a celestial body and move away indefinitely. It is derived from energy conservation, equating the kinetic energy to the gravitational potential energy, and is given by the formula v = ?(2GM/R), where G is the universal gravitational constant, M is the mass of the object, and R is its radius.

Dependence on Radius in Gravitational Fields

In the escape velocity formula, the radius of the celestial body appears in the denominator under the square root. This means that for a fixed mass, a decrease in the radius leads to an increase in the escape velocity because the gravitational field becomes stronger with a smaller radius. This principle is central in understanding how changes in the size of a body affect the energy required to escape its gravitational pull.

Please give Ace some feedback