Solving an Equation using the Gravitational Constant

In summary, if you want to calculate the escape velocity of an object, you need to multiply the gravitational constant by the mass of the object to be escaped from, and then use the sqrt 2() formula.
  • #1
Thrawn
30
0

Homework Statement


Why, in the second step of the question, is 0.001 added to the right side?

Part 2. In the equation Ve = sqrt 2(6.6742 x 10^-11 N m^2 / kg^2 (12.1kg))/0.106780959m

I'm trying to calculate the escape velocity of an object, and have figured out everything up to this point. Now, I have no idea how to procede. Do I cancel things out? Do I add a number to both sides?


Homework Equations


G2.gif





The Attempt at a Solution



For the first part, I would guess that it is simply to... well I have no idea...
 
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  • #2
Thrawn said:

Homework Statement


Why, in the second step of the question, is 0.001 added to the right side?
200 is multiplied by 0.001 to convert it from grams into kilograms, since there are 1000g in 1kg-- does that answer your question?
Part 2. In the equation Ve = sqrt 2(6.6742 x 10^-11 N m^2 / kg^2 (12.1kg))/0.106780959m

I'm trying to calculate the escape velocity of an object, and have figured out everything up to this point. Now, I have no idea how to procede. Do I cancel things out? Do I add a number to both sides?

I don't get what you mean by this!
 
  • #3
cristo said:
200 is multiplied by 0.001 to convert it from grams into kilograms, since there are 1000g in 1kg-- does that answer your question?


I don't get what you mean by this!

The formula to calculate escape velocity is:

Ve = sqrt 2(mu)/r

Where r is the distance from the denter of the object to be escaped from, and mu is the Gravitational Constant multiplied by the mass of the object to be escaped from.

All sai and done, this gives an equation of: Ve = sqrt 2(6.6742 x 10^-11 N m^2 / kg^2 (12.1kg))/0.106780959m

What would be the next step in solving this?
 
  • #4
You just need to check that the units cancel to give a unit of velocity (noting that N=kg m s-2), then compute the numerical answer.
 
  • #5
cristo said:
You just need to check that the units cancel to give a unit of velocity (noting that N=kg m s-2), then compute the numerical answer.


So would the next step be: Ve = sqrt 2(6.6742 x 10^-11 kg m/s^2 m^2/kg^2 (12.1kg)/0.106780959m ?

If not, then what?
 
  • #6
Yes, now check that the units cancel and compute the numerical answer.

Personally, I think the method of keeping the units in during the calculation is very confusing, and that you should convert everything into SI units before plugging into the equation. But ,if that's how you've been taught to answer the question, then I guess you should do it that way.
 
Last edited:

1. What is the value of the gravitational constant (G)?

The value of the gravitational constant is approximately 6.67 x 10^-11 Nm^2/kg^2. This is a fundamental constant in physics that describes the strength of the gravitational force between two objects.

2. How is the gravitational constant used in solving equations?

The gravitational constant is used in equations that involve gravitational force, such as Newton's Law of Universal Gravitation. It is also used in equations that involve the gravitational potential energy between two objects.

3. Can the gravitational constant be changed or varied?

No, the gravitational constant is a fundamental constant and is considered to be a fixed value in our universe. It does not change based on the mass or distance of objects.

4. How is the gravitational constant related to the mass and distance between two objects?

The gravitational constant is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them. This means that as the mass of the objects increases, the gravitational force between them also increases, and as the distance between them increases, the gravitational force decreases.

5. What units are used to measure the gravitational constant?

The gravitational constant is typically measured in units of Newtons times meters squared per kilogram squared (Nm^2/kg^2). However, it can also be expressed in other units such as joules per kilogram meter (J/kgm) or meters cubed per kilogram per second squared (m^3/kg/s^2).

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