How can I calculate the escape velocity of a projectile from a planet's surface?

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Homework Help Overview

The discussion revolves around calculating the escape velocity of a projectile launched from a planet's surface. The original poster presents a problem that requires showing that a projectile with mass "m" can escape if it has a kinetic energy greater than MgR, where R is the planet's radius, while ignoring air resistance. The context includes references to thermal properties of matter, ideal-gas law, and van der Waals equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of escape velocity and its relation to gravitational potential energy and kinetic energy. Some suggest using energy arguments to relate the energies of the projectile at the surface and at escape. There are questions about the relevance of the ideal gas law and how to derive the escape velocity equation.

Discussion Status

The discussion is ongoing, with various participants exploring different interpretations of the problem. Some have offered guidance on using energy conservation principles, while others express confusion about the connections to the ideal gas law. There is no explicit consensus on the approach to take.

Contextual Notes

Some participants note that they have not yet covered the ideal gas law or van der Waals equations, which may limit their ability to connect those concepts to the problem at hand. Additionally, there is uncertainty regarding the definitions and roles of the variables involved in the equations discussed.

CollectiveRocker
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I've been thinking about this for a while now, and I was wanting to know what you guys think. The problem states: Show that a projectile with mass "m" can escape from the surface of a planet if it is launched vertically upward with a kinetic energy greater than MgR, where R is the the planet's radius; ignore air resistance. How do I even start? Its in the chapter deal with "thermal properties of matter; thus the ideal-gas law and van de waals equation". Any ideas?
 
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no...
go to the index of the book and search for "escape velocity"
 
I already know that escape velocity is the velocity which it takes to escape a planet's gravitational pull, for example, Earth is around 22,500 mph.
 
okke
escape velocity ,v= (2 * G * M / R) ^(1/2) ...(1)

Kinetic energy , KE = 1/2 mv^2

[
now g = GM/R^2
therefor GM = gR^2 ... (2)
]

KE = 1/2 m (2 G M / R) [ from ... (1) ]
= GM * m / R
= gR^2 *m / R [ from 2 ]
= mgR

M maybe is m
 
yes M is m, but how does that solve the problem?
 
So what do i do now?
 
If M = m ,than what do i do?
 
CollectiveRocker said:
I've been thinking about this for a while now, and I was wanting to know what you guys think. The problem states: Show that a projectile with mass "m" can escape from the surface of a planet if it is launched vertically upward with a kinetic energy greater than MgR, where R is the the planet's radius; ignore air resistance. How do I even start? Its in the chapter deal with "thermal properties of matter; thus the ideal-gas law and van de waals equation". Any ideas?

derive the equation for escape velocity

K(i) = -U(g)

you have a given K(i) is it > -U(g)?

we haven't covered the ideal gas law or van der waals equations yet, though.
 
I don't understand what you are saying. Please explain if possible in laymans terms.
 
  • #10
This problem has nothing to do with the Ideal Gas Law and such. It's simple classical Newtonian physics.

Use an energy argument. Find the energy of an object that has escaped from the gravitational field of Earth (hint: it's 0), and find the energy of the car on the ground. This two energies must be equal.

Just keep in mind that the car on the ground has two energies associated with it, the potential energy due to the gravitational field (this energy is negative), and the kinetic energy due to the movement of the car.

--J
 
  • #11
CollectiveRocker said:
I don't understand what you are saying. Please explain if possible in laymans terms.

well think about escape velocity and how you can derive it from conservation of energy

your initial velocity is the escape velocity, so at a certain time when you're so far away from the planet that your velocity is zero, and its force on you is zero.

in that case you've got

K(i) + U(g) = 0

where K(i) is your initial kinetic energy and U(g) is the potential gravitational energy.

by simple algebra

K(i) = -U(g)

if you calculate this you can derive the formula for escape velocity.

now, you know that you have a kinetic energy greater than MgR (or something like that, right?)

so substitute your values for the equation above

your K(i) > -U(g)

this is saying that your initial kinetic energy is greater than the potential gravitational energy of the planet.

does that make sense? i think it would work
 

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