Kinetic Energy Problem?

Question

Calculate the KE of an asteroid that is 10km across, has a desnity of 5 metric tons/m^3, and slams into the earth at 69,000mi/hr.

The equation is supposedly:
KE at impact= 0.5mv^2
But I don't understand how I'm supposed to do it.

Thanks for your help ^^

Answer 1

If it is a sphere, use the equation for volume 4/3 pi r cubed or something, to find volume. But make sure you convert the 10 km to meters (use 10000 in your calculation) (btw r = .5 d) Then, multiply that volume by the density to get the mass in metric tons, then convert to whatever you are comfortable with, kg are usually used, and use that for the m in .5 mv squared. For the v, convert 69000 mi/hr to m / second, so use conversion factors.

Answer 2

There are two tricky parts. First, you need to convert these measures into one standard -- let's keep metric. Second, you need to assume the shape of the asteroid. Let's assume it's spherical for lack of other information. SO the mass of the asteroid is

the volume times the density. The volume is 4/3 π r^3 wher r=5 km or 5000 m. THe volume is therefore 4/3 π (5000)^3=523.6E6 m^3

5 metric tons/m^3 is 5000 kg/m^3. So the mass is 2.62E14 kg.

69,000 mi/hr in m/s is (69,000)*(1609.3 m/mi)*(1/3600 hr/s)=30844.9 m/s

Putting it all together we get

1/2(2.62E14)(30844.9)^2=1.25E23 J

Answer 3

Well, you would have to factor out the energy lost due to the asteroid impacting the atmosphere first....This would involve knowing the dimensions of the asteroid, it's features, angle of trajectory etc. Co-efficient of drag and all that good stuff....