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

In summary, the conversation discusses whether the work done by gravity on an approaching meteor is positive or negative. The formula W(1->2) = integral (1->2) F(gravity) dot dr is used, resulting in a positive value due to the larger denominator in the second term. The concept of dot products and their relationship to the direction of motion and change in position vector is also explored. It is concluded that the work done by gravity is negative, resulting in a decrease in the meteor's velocity.
  • #1
Ben Harris
4
1
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
 
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  • #2
Ben Harris said:
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?
 
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  • #3
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!
 
  • #4
More generally, ΔW = |F| |Δs| cosθ is negative when 90o < θ ≤ 180o.
Ben Harris said:
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.
 
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  • #5
Ohhhhhh Yes!, that is correct... it will be negative!

Thank you for making me work for the answer :)
 
  • #6
If the work done by gravity is negative the velocity of the meteor should decrease, shouldn't it?
 
  • #7
nasu said:
If the work done by gravity is negative the velocity of the meteor should decrease, shouldn't it?
Yes.
 
  • #8
kuruman said:
Yes.
The question was for the OP. :)
 
  • #9
nasu said:
The question was for the OP. :)
Sorry, I was in autopilot. :sorry:
 

1. Is the work done on a meteor approaching the Earth positive or negative?

The work done on a meteor approaching the Earth depends on the reference frame. If we are considering the Earth as the reference frame, then the work done is negative as the meteor is moving towards the Earth. However, if we consider the meteor as the reference frame, then the work done is positive as the Earth is moving towards the meteor.

2. How is the work done on a meteor approaching the Earth calculated?

The work done on a meteor approaching the Earth can be calculated using the formula W = Fd, where W is the work done, F is the force acting on the meteor, and d is the distance traveled by the meteor. The direction of the force and the distance traveled will determine if the work done is positive or negative.

3. Does the mass of the meteor affect the work done on it as it approaches the Earth?

Yes, the mass of the meteor does affect the work done on it as it approaches the Earth. The greater the mass of the meteor, the more force is required to stop it, resulting in a larger amount of work being done.

4. Can the work done on a meteor approaching the Earth be converted into other forms of energy?

Yes, the work done on a meteor approaching the Earth can be converted into other forms of energy, such as thermal energy or sound energy, upon impact with the Earth's surface. This conversion of energy follows the law of conservation of energy.

5. How does the angle of approach of a meteor affect the work done on it as it approaches the Earth?

The angle of approach of a meteor does affect the work done on it as it approaches the Earth. If the meteor is approaching at a perpendicular angle, the work done will be greater as the force acting on the meteor is directly opposing its motion. However, if the meteor is approaching at an angle, the work done will be less as the force acting on the meteor is not directly opposing its motion.

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