Exploring Magnetism in Solar Flares - worksheet 4.6 solutions

Worksheet 4.6 (Teacher's Answers)

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The blob that was ejected from the solar flare later moved completely away from the Sun as a Coronal Mass Ejection (CME) moving with the same speed that you calculated in Worksheet 4.5. This blob has mass and a speed, so we can calculate its kinetic energy. The formula for kinetic energy is:

KE = ½mv²
where m is mass and v is speed.
(Note: v is used for velocity, which is speed and direction, but in this formula there is no direction, so speed and velocity are the same.)

1.		The mass of the blob can be estimated by first estimating its volume and using the typical density of plasma in a coronal loop. Examine the 9th flare image in the series (23:12:50.50 UT) and estimate the diameter of the blob in kilometers. Show your work and record the number below. Diameter of blob = 1 cm 1 cm x 11 arcsec/cm = 11 arcsec 11 arcsec x 725 km/arcsec = 7,975 km

2.		Assume that the blob is a sphere and calculate its volume. Show all work. V = 4/3 πr3 r = D/2 = 7975 km/2 = 3988 km V = 4/3 x π x (3988 km)3 = 2.66 x 1011 km3

3.		The typical density of plasma in a coronal loop is 2 x 10-14 g/cm3. Use this value to calculate the mass of the blob. Show all work. m = ρV V = 2.66 x 1011 km3 x (105 cm/km)3 = 2.66 x 1026 cm3 m = 2 x 10-14 g/cm3 x 2.66 x 1026 cm3 = 5.32 x 1012 g

4.		Now, calculate the kinetic energy of the blob in Joules. Show all work, and be mindful of units. KE = ½ mv2 m = (5.32 x 1012 g) x 1 kg/103g = 5.32 x 109 kg v = 240 km/s x 103 m/km = 2.4 x 105 m/s KE = 0.5 x (5.32 x 109 kg) x (2.4 x 105 m/s)2 = 1.53 x 1020 kg m2/s2 = 1.53 x 1020 Joules

5.		The actual amount of mass that was ejected from the Sun was 10 times larger than just that seen in the X-ray image. The total amount of mass ejected from the Sun was estimated by NASA scientists to be 5 x 1013 g. Calculate the kinetic energy of the CME in Joules. Show all work and be mindful of units. m = (5 x 1013 g) x 1 kg/103g = 5 x 1010 kg v = 2.4 x 105 m/s KE = 0.5 x (5 x 1010 kg) x (2.4 x 105 m/s)2 = 1.44 x 1021 kg m2/s2 = 1.44 x 1021 Joules.

6.		The total amount of energy released by the flare that went into heating and accelerating matter was estimated by NASA scientists to be 2 x1023 Joules. How does this compare to the amount of kinetic energy given to the CME? How many candy bars would you have to eat to equal the total amount of energy? Show all work and be mindful of units. 1.44 x 1021 Joules / 2 x 1023 Joules = 0.0072 = 0.7% of total flare (rather small) 1 candy bar = 250 Calories 250 Cal x 4,186.8 Joules/Cal = 1.05 x 106 Joules 2 x 1023 Joules x (1 Candy Bar)/(1.05 x 106 Joules) = 1.9 x 1017 candy bars That’s 190 quadrillion candy bars. Whew!