What is the weight on a planet with twice the mass and radius of Earth?

[pinkey]

Homework Statement

A person weighing 800N on Earth travels to another planter with twice the mass and twice the radius of the Earth. The person's weight on this other planet is most nearly...

earth radius is 6,380,000m
earth mass is 5,970,000,000,000,000,000,000,000kg

Homework Equations

What is the person's weight on the other planet?

The Attempt at a Solution

I thought it was still 800N because everything was doubled so it would proportionally be the same. It turns out the answer is 400N and I was hoping someone could explain why that is.

thanks to anyone who tries.

 

[learningphysics]

suppose m1 is the mass of the person. me is the mass of the earth... re is the radius of the earth

so Fe = Gm1me/re^2, where Fe is the gravitational force on the earth.

What is the gravitational force on the person when he's on the other planet?

Fp = Gm1mp/rp^2

we know that mp = 2me. rp = 2re

Fp = Gm1(2me)/(2re)^2

take all the constants out to the left... so that this has the form:

Fp = k*Gm1me/re^2
Fp = k*Fe

what is k?

 

[pinkey]

thanks, so you're supposed to answer the question without any numbers first? i understand what you wrote up until the k part. is k 2?

 

[learningphysics]

thanks, so you're supposed to answer the question without any numbers first? i understand what you wrote up until the k part. is k 2?

No, k isn't 2. Try to manipulate:

Fp = Gm1(2me)/(2re)^2

simplify this... We don't want those 2's like that... we just want a numerical constant out to the left...

 

[pinkey]

is k the person's mass? Because that is supposed to be constant.

 

[learningphysics]

Another way to approach this is: take the ratio of Fp/Fe.

Fp/Fe = [Gm1(2me)/(2re)^2]/[Gm1me/re^2]

simplify the right side... try to cancel everything that you can... what is Fp/Fe come out to?

 

[learningphysics]

is k the person's mass? Because that is supposed to be constant.

no k isn't the person's mass... m1 is the person's mass...

simplify:

Fp = Gm1(2me)/(2re)^2

 

[pinkey]

can't you cancel everything out except the 2s, then that's just 2/2?

 

[learningphysics]

can't you cancel everything out except the 2s, then that's just 2/2?

don't forget about the squared part... (2re)^2 etc...

 

[learningphysics]

don't take any shortcuts... work through it...

 

[pinkey]

So I could get rid of the 2s and have that:

Fp = Gm1(me)/(re)^2

but then what else could i simplify?

 

[learningphysics]

So I could get rid of the 2s and have that:

Fp = Gm1(me)/(re)^2

but then what else could i simplify?

Fp = Gm1(2me)/(2re)^2

Fp = Gm1(2me)/(4re^2)

Fp = Gm1me/(2re^2)

Fp = (1/2)[Gm1me/r^2]

Fp = (1/2)*Fe

 

[pinkey]

oh my god! that's so good. thank you so much!

 

[learningphysics]

oh my god! that's so good. thank you so much!

no prob. careful of those squares.