Stuck (Kinetic Energy & Pressure of Meteoroids)

[spinnaker]

Hi there,

I'm helping tutor a friend in astrophysics and I've come across a question I can't answer - which is annoying and embarassing to say the least :)

The question reads:

(a) Calculate the kinetic energy and pressure involved when the Earth gets hit by a stony meteoroid (ρ = 3400 kg/m³) that has a diameter of 10km and a zero velocity at a very large distance from the Earth.

(b) Calculate the kinetic energy and pressure involved if the same meteoroid were to hit Jupiter instead of the Earth, assuming the body has zero velocity at a large distance from Jupiter

(c) Calculate the kinetic energy and pressure involved when a fragment of Comet D/Shoemaker-Levy 9 (ρ = 500 kg/m³, R = 0.5km) hits Jupiter at the planet's escape velocity.

My problem is the zero velocity at a very large distance from the Earth. I can't figure out a reference point from which I can calculate total energy -- 1/2mv^2 means nothing at zero velocity, and "large distance" tells me nothing for calculating total energy.

Any help/hints/tips would be appreciated!

 

[tms]

My problem is the zero velocity at a very large distance from the Earth. I can't figure out a reference point from which I can calculate total energy $\ldots$

In cases of gravitation, it is usual to pick the zero point of potential energy to be at infinity.

$\ldots$ -- 1/2mv^2 means nothing at zero velocity,

Having a value of zero is not the same as meaning nothing.

 

[spinnaker]

Fair enough, I've been tinkering and I think I found my initial issue. I made 0 = 1/2mv^2 -GM(earth)m(asteroid)/r(earth) and I get 8.88e23 J, which is realistic. Equates to an impact of about 11km/s.

I still don't know what they mean by pressure involved, though.

 

[tms]

I'm not sure what they want for the pressure, either. Obviously the force per unit area of the collision, but which area? The entire cross-sectional area of the Earth, or just the immediate area of the impact? I would guess the former, but I'm not positive.

 

[HalfLostAndSearching]

Hi there,

I can understand your frustration with this question. Calculating the kinetic energy and pressure of meteoroids can be a complex task, but there are some key concepts that can help guide you in finding the answers.

First, let's define some terms. Kinetic energy is the energy an object possesses due to its motion, and is calculated using the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity. Pressure, on the other hand, is a measure of the force exerted per unit area and is calculated using the formula P = F/A, where F is the force exerted and A is the area over which the force is exerted.

Now, to address your concerns about the zero velocity at a large distance. In this situation, we can assume that the meteoroid has been pulled towards the Earth (or Jupiter) by gravity and has reached a velocity of zero at a large distance. This means that at the point of impact, the meteoroid will have a velocity of zero. However, at a large distance, the meteoroid will still have some potential energy due to its position in the gravitational field.

To calculate the total kinetic energy, we can use the concept of conservation of energy. This means that the total energy (kinetic + potential) at the point of impact will be equal to the total energy at the initial point. So, to calculate the kinetic energy at the point of impact, we can subtract the potential energy at the initial point from the total energy at the initial point.

I hope this helps guide you in solving the problem. Remember to consider the mass and velocity of the meteoroid, as well as the gravitational potential energy at the initial point, to calculate the total kinetic energy and pressure at the point of impact. Best of luck with your tutoring session!