# Work done on a meteor approaching the Earth -- Is it +ve or -ve?

Hi all, i am trying to figure out if work done by gravity is positive or negative on an approaching meteor,

I have used W(1->2) = integral (1->2) F(gravity) dot dr. and got a result of (GMem/r2) - (GMem/r1).

Were G is gravity, Me is earth mass, m is meteor mass and r1, r2 are initial and final radius respectively.

As (GMem/r2) > (GMem/r1) the result has to be positive right?

any help is appreciated :)

thank you

kuruman
Homework Helper
Gold Member
Hi all, i am trying to figure out if work done by gravity is positive or negative on an approaching meteor,

I have used W(1->2) = integral (1->2) F(gravity) dot dr. and got a result of (GMem/r2) - (GMem/r1).

Were G is gravity, Me is earth mass, m is meteor mass and r1, r2 are initial and final radius respectively.

As (GMem/r2) > (GMem/r1) the result has to be positive right?

any help is appreciated :)

thank you
It's simpler than that. The work done by a force on an object is ##dW=\vec F \cdot d\vec s##. The total work is the sum of all such terms. To find the sign of the work, you need to figure out when a dot product is positive and when it is negative. Any ideas?

Ben Harris
Thanks Kuruman,

So if the vectors of F & Δs are opposite (180) then the result is negative when using ΔW = |F| |Δs| cos 180.

I think i was getting confused between the direction of motion vs the change in position vector.

kuruman
Homework Helper
Gold Member
More generally, ΔW = |F| |Δs| cosθ is negative when 90o < θ ≤ 180o.
I think i was getting confused between the direction of motion vs the change in position vector.
Are the two different? The direction of motion is the same as the direction of the velocity vector. The velocity vector is defined as ##\vec v = \frac{d \vec s}{dt}## therefore ##\vec v## and ##d\vec s## point in the same direction.

Ben Harris
Ohhhhhh Yes!, that is correct.......... it will be negative!

Thank you for making me work for the answer :)

nasu
Gold Member
If the work done by gravity is negative the velocity of the meteor should decrease, shouldn't it?

kuruman
Homework Helper
Gold Member
If the work done by gravity is negative the velocity of the meteor should decrease, shouldn't it?
Yes.

nasu
Gold Member
Yes.
The question was for the OP. :)

kuruman