A comet is traveling towards the earth. The comet has a mass of 5.50E+12 kg and a radius of 323 m. The comet is traveling with a speed of 13.5 km/s and spinning with a period of 0.15 seconds when its center is a distance 2.28E+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 7.9 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.
To determine the total amount of energy converted to thermal energy, we need to calculate the change in kinetic energy of the comet as it moves through the atmosphere.
First, let's calculate the initial kinetic energy of the comet. The kinetic energy of an object can be calculated using the formula:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
The initial mass of the comet is given as 5.50E+12 kg and its initial velocity is 13.5 km/s.
Converting the velocity to meters per second:
v_initial = 13.5 km/s * 1000 m/km = 13500 m/s
Calculating the initial kinetic energy:
KE_initial = (1/2) * (5.50E+12 kg) * (13500 m/s)^2
Next, let's calculate the final kinetic energy of the comet just before it strikes the surface of the earth. The final velocity of the comet is given as 7.9 km/s.
Converting the velocity to meters per second:
v_final = 7.9 km/s * 1000 m/km = 7900 m/s
Calculating the final kinetic energy:
KE_final = (1/2) * (5.50E+12 kg) * (7900 m/s)^2
Now, we can determine the change in kinetic energy:
ΔKE = KE_final - KE_initial
Finally, the total amount of energy converted to thermal energy can be taken as equal to the change in kinetic energy, since no other forms of energy are mentioned in the question.
To calculate the total amount of energy converted to thermal energy, you need to subtract the initial kinetic energy from the final kinetic energy:
Total thermal energy = ΔKE = KE_final - KE_initial
I will calculate the final kinetic energy and then subtract the initial kinetic energy to find the change in kinetic energy.