See National Math and Science Standards for this Challenge.
Q: How much energy will be produced when the impactor hits Tempel 1?
In order to reduce costs, the Mission Team decided to go with a slightly smaller launch rocket. That meant that they had to reduce the overall mass of the flight system. One of the places where they were able to reduce mass was on the impactor. The mass of the impactor was changed from 500kg to 350 kg. The scientists were concerned though because this means that the amount of energy produced at impact will be reduced as well. Help us figure out how much energy is produced at impact with the 350 kg impactor!
Update: In the spring of 2002, the mass of the impactor was increased from 350kg to 370 kg. How will the extra 20 kilos affect the amount of energy produced?
Hints:
Mass of the impactor: m = 370 kg
Velocity of the impactor: v = 10.2 km/s
A: To calculate the answer, you should first determine what information you have, what formula(s) to use, and in what units the answer should be given.
What do we know? From the website, we know:
Mass of the impactor: m = 370 kg
Velocity of the impactor: v = 10.2 km/s
What formula should we use? That's a bit tougher since it's not in the website. It helps to know a little bit of physics, but we'll help!
Formula to use: kinetic energy = 1/2 (mv2)
Plugging in the numbers
KE= 1/2 (370kg (10.2 km/s)2 )
= 19247.4 kg·km2/s2
But in the website the answer says 19 Gigajoules. If we look up Joules, we find that 1 J = 1 kg·m2/s2 (meters not km) so we need to go back and convert the velocity from km/s to m/s and we get v = 10200 m/s.
Plugging in the numbers again
KE= 1/2 (370kg (10200 m/s)2 )
= 1.92 × 1010 kg·m2/s2 or 1.92 × 1010 J
1 GJ = 109 J
therefore, KE = 19 GJ
But how much is 19 GJ? Well, it turns out that 1 Megaton of TNT (or 1 million tons of TNT) is equivalent to 4 × 1015 J.
Some more converting:
19 GJ = 19 × 109 J × (1 × 106 tons TNT/4 × 1015 J)
the joules cancel, 109 × 106/1015 cancels leaving
= 19/4 tons of TNT
= 4.8 tons of TNT
