Calculating Impact Energy: 1km Asteroid at 20km/s = X Megatons of TNT

[Alyshea]

1. An asteroid of 1.0 km diameter will make a crater of about 10 km diameter. How much kinetic energy does the asteroid have if it strikes the surface at about 20km/s. Convert answers to megatons of TNT; 1 megaton = 4 X 10^15 Joules.



2. I do not understand how there is enough information given to solve this problem. I know that KE= (1/2) mv^2 but I do not know the mass. So I tried to find the mass of a circle, but then you need density, which I also do not have. I am completely lost.



3. Any suggestions would be helpful! Thank you

 

[berkeman]

1. An asteroid of 1.0 km diameter will make a crater of about 10 km diameter. How much kinetic energy does the asteroid have if it strikes the surface at about 20km/s. Convert answers to megatons of TNT; 1 megaton = 4 X 10^15 Joules.



2. I do not understand how there is enough information given to solve this problem. I know that KE= (1/2) mv^2 but I do not know the mass. So I tried to find the mass of a circle, but then you need density, which I also do not have. I am completely lost.



3. Any suggestions would be helpful! Thank you

You're correct that you need the mass. I'd just google asteroid density, and see what the range is. Maybe calculate a range of energies, based on the range of densities that you find.

 

[Alyshea]

OK so even if I get the approx density, I need the volume as well to calculate mass right?

 

[berkeman]

OK so even if I get the approx density, I need the volume as well to calculate mass right?

Yes. Luckily, you are given at least that.

 

[Alyshea]

I am? I'm sorry I have not taken a science class in over 6 years, I am a single mom returning to college so all of this is way over my head.

 

[Alyshea]

Wait is this it? (4/3) * pi * radius^3

 

[berkeman]

Wait is this it? (4/3) * pi * radius^3

Good!

 

[Alyshea]

Thank you so much!

 

[berkeman]

I googled asteroid density, and got lots of good hits. Here's the first one:

http://homepage.mac.com/brother_guy/.Public/Asteroid%20Densities.pdf

It shows a chart with a wide distribution of densities (yikes), but an average around 2.4 grams/cc. You need to convert that into the mks system of units, which is meters, kilograms, seconds.

To convert from g to kg, use the identity 1000g = 1kg.

To convert from cubic centimeters, use the identity 100cm = 1m, and cube both sides.

It's a good idea to carry units along in your equations, especially when you are converting units. Cancel any units that appear on both top and bottom of a fraction, just as you would cancel 5/5 and turn it into 1.

So to convert 3cm to meters, I multiply 3cm by 1 like this:

3cm * (1m/100cm) = 3cm*m/100cm = 3m/100 = 0.03m

You will have to figure out the other conversions that are mentioned in the problem. The key to doing conversions well is to figure out the identity equation (how many of one thing equals the other thing), and then just multiply whatever you want to convert by 1 (the special 1 you get from your identity equation).

Hope that helps. Welcome to the PF, BTW.

 

[Alyshea]

Wow, thank you so much. I really appreciate it.