Calculating Velocity of Meteor Rock Fragment Falling on Neptune

In summary, the conversation discusses a homework problem involving a meteor rock fragment at rest above Neptune's surface and the work done by Neptune's force of gravity as the rock falls to the planet's surface. The answer for the work done is 3.74x10^10J. The conversation then moves on to finding the velocity with which the rock strikes Neptune's surface. The correct answer is 7.7x10^3, which was calculated using conservation of energy and the equation 3.74x10^10J = 1/2mv^2. The mistake in the calculation was forgetting to multiply by 2.
  • #1
Avis
42
0

Homework Statement



A 1250kg meteor rock fragment is momentarily at rest at an altitude of 3000km above the surface of Neptune. Neptune has a mass of 1.03x1026kg and a radius of 2.48x107m.

Determine: how much work is done on the rock by Neptunes Force of gravity as the rock falls to Neptunes surface (I got the answer to this one it was 3.74x1010J

I need help on: the velocity with which the rock strikes Neptunes surface

Not sure where to start with this one.
 
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  • #2
If you can find the gravity on Neptune, you can use conservation of energy to determine it's velocity.
 
  • #3
so:
W=Ek
3.74x10^10j=1/2mv^2
3.74x10^10j=1/2(1250kg)v^2
v= (square root of) 3.74x10^10j/1250kg
= 7.7X10^4

But the answer says 7.7X10^3

Where did i go wrong?
 
  • #4
The 1/2 magically disappeared. :) You just forgot to multiply by 2, but you got essentially.
 
  • #5
i screwd up there... when i take half of the 1250kg i get the answer above.
 

Related to Calculating Velocity of Meteor Rock Fragment Falling on Neptune

1. How is the velocity of a meteor rock fragment falling on Neptune calculated?

The velocity of a meteor rock fragment falling on Neptune is calculated using the formula v = √(2gh), where v is the velocity, g is the gravitational acceleration on Neptune, and h is the height from which the fragment falls. This formula assumes that there is no air resistance.

2. What is the gravitational acceleration on Neptune?

The gravitational acceleration on Neptune is approximately 11.15 m/s². This is significantly higher than the gravitational acceleration on Earth, which is 9.8 m/s².

3. How does the mass of the meteor rock fragment affect its velocity?

The mass of the meteor rock fragment does not significantly affect its velocity as long as the same formula is used. This is because the mass of an object does not affect its acceleration due to gravity.

4. Can the velocity of a meteor rock fragment falling on Neptune be affected by air resistance?

Yes, the velocity of a meteor rock fragment falling on Neptune can be affected by air resistance. However, since Neptune has a very thin atmosphere, the effect of air resistance is minimal and can be ignored for most calculations.

5. Is there a maximum velocity that a meteor rock fragment can reach while falling on Neptune?

Yes, there is a maximum velocity that a meteor rock fragment can reach while falling on Neptune. This is known as the terminal velocity, which is the maximum velocity an object can reach when the force of air resistance is equal to the force of gravity. However, since the atmosphere on Neptune is so thin, the terminal velocity for a meteor rock fragment is much higher than on Earth.

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