# Comet Crashes in Earth Conservation of Energy

Tags:
1. Oct 29, 2012

### kchurchi

1. The problem statement, all variables and given/known data

A comet is traveling towards the earth. The comet has a mass of 4.80E+12 kg and a radius of 385 m. The comet is traveling with a speed of 19 km/s and spinning with a period of 0.12 seconds when its center is a distance 1.88E+7 m away from the center of the earth. The comet is roughly spherical, so its moment of inertia will be that of a uniform, solid sphere. Just before the comet strikes the surface of the earth, its speed is 10.1 km/s, and its rotation is essentially zero. Use the following values for constants
G = 6.673E-11 N m2/kg2
mass of earth = 5.976E+24 kg
radius of earth = 6.378E+6 m

A lot of energy is converted to thermal energy as the comet travels through the atmosphere. Using the information above, determine the total amount of energy converted to thermal energy.

2. Relevant equations
W(tot) = deltE(sys)
deltU(g) = -G*mE*mC/r(f) + G*mE*mC/r(i)
deltK(translational) = 1/2*mC*v(f)^2 - 1/2*mC*v(i)^2
deltK(rot) = 1/2*I*omega(f)^2 - 1/2*I*omega(i)^2
I = I(sphere)

3. The attempt at a solution
I have the right equation, several TA's have already checked it. But for some reason I cannot get the right answer. I solved for the change in thermal energy by taking the system to be everything so work is 0. Then I said the energy of the system is equal to the potential energy of gravity + the kinetic energy of rotation + the kinetic energy of translation + thermal energy. I just brought all terms except thermal energy to the other side and solved. What am I doing wrong?

Equation:
deltE(therm) = -deltU(g) - deltK(rot) - deltK(trans)
deltE(therm) = -(-G*mE*mC/(rE+rC) + G*mE*mC/r(i)) -(1/2*I*omega(f)^2 - 1/2*I*w(i)^2) - (1/2*mC*v(f)^2 - 1/2*mC*v(i)^2)

v(i), v(f), mE, mC, rE, rC, r(i), G, period (T), and I are given
I(sphere)= 2/5*(mC/(rC^2))
omega(f) = 0
omega(i) = 2*pi/T

2. Oct 29, 2012

### Staff: Mentor

Do you have individual values for deltU(g), deltK(rot), deltK(trans)? What is your final result, what is the correct result?
The equations look fine.

The comet has twice the density of lead, but well...