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

[Ben Harris]

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]

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.

Thank you for your help!

 

[kuruman]

More generally, ΔW = |F| |Δs| cosθ is negative when 90^o < θ ≤ 180^o.

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]

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

 

[kuruman]

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

Yes.

 

[nasu]

Yes.

The question was for the OP. :)

 

[kuruman]

The question was for the OP. :)

Sorry, I was in autopilot.