Question Regarding potential energy (1 Viewer)

[AnimeX]

How do you do this question?

" Calculate the energy required to lift Peter (mass 70kg) to a location where Earth's gravitational field is negligible"

I'm unsure of the radius to use in the Ep formula, it won't be zero? what would it be?

 

[seanieg89]

 

[AnimeX]

I think there's an actual numerical value~



Would r= radius of earth work?

My logic at the moment:

Ep is the gravitational potential energy required to move an object (Peter) from infinity to a point (earth) = -GMm / r = - G M(earth) m(peter) / r(earth)

So therefore to the kinetic energy required to get peter to infinity would be = GMm / r = G M(earth) m(peter) / r(earth), since gravitational potential energy + kinetic energy = 0

 

[someth1ng]

Remember that gravitational potential energy is the amount of energy needed to move an object from an infinite distance away to a point in the gravitational field (negative).

Therefore, the energy required to move the object to an infinite distance away is just its gravitational potential energy, except positive in magnitude - if it took you -X energy to get here, it'll take you X energy to get back to where you started.

Method 1: Using GPE
U(g)=-Gm1m2/d
U(g)=-6.67x10^-11x[(70x5.97x10^24)/(6400x10^3)]
U(g)=-4.36x10^9J
E=4.36x10^9J

Method 2: Using Escape Velocity
v(escape)=root(2GM/r)
v(escape)=root[2(6.67x10^-11)(5.97x10^24)/6400000]
v(escape)=11155m/s

E=0.5mv^2
E=0.5x70x11155^2
E=4.36x10^9J

 

[nightweaver066]

Remember that gravitational potential energy is the amount of energy needed to move an object from an infinite distance away to a point in the gravitational field (negative).

Therefore, the energy required to move the object to an infinite distance away is just its gravitational potential energy, except positive in magnitude - if it took you -X energy to get here, it'll take you X energy to get back to where you started.

U(g)=-Gm1m2/d
U(g)=-6.67x10^-11x[(70x5.97x10^24)/(6400x10^3)]
U(g)=-4.36x10^9J
.'. The energy required to bring an object to infinity is 4.36x10^9J

Fixed:

I'm too bored lol

 

[someth1ng]

Fixed:

I'm too bored lol

I guess that looks a fair bit prettier LOL.

 

[AnimeX]

Yep, thanks someth1ng and nightweaver! makes sense haha.

Any reason why you guys use U(g)? i believe wiki uses that too

 

[someth1ng]

U means potential energy in university.

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[AnimeX]

U means potential energy in university.

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Ahh ok.