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The answer sheet for the worksheet The energy of impacts and airbursts. Each answer comes with the reason, so it can be used to mark or to go over the questions with the class.

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A-level · Ages 16 to 18 (Years 12 and 13)Answer sheet for teachers

Answers: The energy of impacts and airbursts

  1. D: Gravity and target strength limit how much rock can be excavatedThe energy must excavate and lift a volume of rock against gravity and the rock's strength, so diameter scales only as about E^(1/4) to E^(1/3).
  2. B: It fragments and explodes in the atmosphereStony bodies up to a few tens of metres usually break up and release their energy as an airburst, as at Chelyabinsk.
  3. A: About 2.1 × 10¹⁵ JMultiply by the joules in one megatonne: 0.5 × 4.184 × 10¹⁵ J ≈ 2.1 × 10¹⁵ J, consistent with the worked calculation from its mass and speed. Dividing instead of multiplying gives the tiny wrong value.
  4. A: About 2.6 timesAt fixed size the mass, and so E = ½mv², is proportional to density: 7,800 ÷ 3,000 = 2.6.
  5. C: They collapse under gravity into complex cratersAbove a few kilometres on Earth, the transient crater collapses under gravity, giving a complex crater.
  6. True (1 kt blast, Chelyabinsk, 50 m stony body at 17 km s⁻¹, Tunguska)Chelyabinsk was about 0.5 Mt (500 kt), the 50 m stony body carries about 7 Mt, and Tunguska released about 10 to 15 Mt.
  7. True (Iron is denser and much stronger, so it can reach the ground)The iron body has about 2.6 times the mass and energy, and its strength lets it survive to the ground, while a 50 m stony body tends to burst in the air.
  8. A sphere's volume is (4/3)πr³, and r = d/2 (accept any answer with the same meaning)(4/3)π(d/2)³ = (4/3)π × d³/8 = (π/6)d³; multiplying this volume by density gives the mass.
  9. 4 (accept any answer with the same meaning)E = ½mv², so energy is proportional to v²: doubling the speed multiplies the energy by 2² = 4.
  10. About 48 kt (accept any answer with the same meaning)E = ½ × 1.0 × 10⁶ × (2.0 × 10⁴)² = 2.0 × 10¹⁴ J, and 2.0 × 10¹⁴ ÷ 4.184 × 10¹² ≈ 48 kt.

Task

Answers will vary. The task comes from the lesson: Use the impact calculator on this site to find the energy of a 50 m stony body (density 3,000 kg m⁻³) at 17 km s⁻¹, then check it by hand. Repeat for an iron body (7,800 kg m⁻³). Explain why the outcomes predicted by the calculator differ so much for the two compositions.

Look for work that uses the key words correctly and gives a reason for each point.

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