What is the required energy for a projectile to escape Earth?

[mrdrew]

I have a 3 part question, and I have managed to get 2 of the three parts, but I can not figure out the 3rd for the life of me.
A projectile is shot directly away from Earth's surface. Neglect the rotation of Earth. (C) What is the least initial mechanical energy required at launch if the projectile is to escape earth?

I kind of thought i should be using the escape speed of Earth (11.2 km/s or 11200 m/s) and calculate Ek. However, I have no mass, so I'm not quite sure if that's the right way to approach the problem. Any thoughts?

Many thanks!

 

[Tide]

What is the TOTAL energy of the projectile when it is launched. What is the potential energy of the projectile if it "just reaches" infinity with 0 speed?

 

[Vector Sum]

Yet you still need the mass of the projectile to know total energy.

If the mass is not given, you can provide the answer as a number "times m." But, I'm guessing that perhaps the mass could have been determined from the first part(s) of the question?

 

[BobG]

I have a 3 part question, and I have managed to get 2 of the three parts, but I can not figure out the 3rd for the life of me.
A projectile is shot directly away from Earth's surface. Neglect the rotation of Earth. (C) What is the least initial mechanical energy required at launch if the projectile is to escape earth?

I kind of thought i should be using the escape speed of Earth (11.2 km/s or 11200 m/s) and calculate Ek. However, I have no mass, so I'm not quite sure if that's the right way to approach the problem. Any thoughts?

Many thanks!

Yes, you're going the right direction. Total mechanical energy = kinetic plus potential.

As to not having the mass, check your terminology in the book. Usually, if they're talking launches and escape velocity, they're concentrating on how the object moves (acceleration) vs. its 'true' total energy. Since the mass cancels out for acceleration, it's very common for them to talk about 'specific energy' per unit of mass. Either way, if you don't have the mass, the best you can do is express the answer as the 'specific energy times mass'.

$$m\epsilon$$

 

[mrdrew]

im not quite sure i understood exactly what you were referring to when it comes to acceleration of the object. the question in its entirety is here.

a projectile is shot directly away from Earth's surface. Neglect the rotation of Earth. What multiple of Earth's radius Re gives the radial distance a projectile reaches if (a) its initial speed is 0.500 of the escape speed from Earth and (b) its initial kinetic evergy is 0.500 of the kinetic energy required to escape earth? (c) what is the least initial mechanical energy required at launch if the projectile is to escape earth?

i was just thinking, is there a specific distance away from the Earth where a projectile has successfully 'escaped' Earth's gravitational field, or is that mass depenedent as well. If it wasn't, i suppose i could find the gravitational energy at that point and then use to equate it to the necessary kinetic force to get to that distance?