Howardites

Worksheet for the lesson Energy and crater size: does doubling the energy double the crater? (GCSE (Years 10 and 11)). Printing gives the pupil copy; open the answers below first to print them as a teacher copy on a separate page.

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Energy and crater size

Name:Date:

Mass of ball: ______ kg. g = 9.8 N/kg. Ep = m × g × h. Measure each crater rim to rim in two directions at right angles.

Height h (m)Ep (J)Diameter 1 (cm)Diameter 2 (cm)Repeat 1 (cm)Repeat 2 (cm)Mean diameter (cm)
0.10
0.20
0.40
0.80
1.20

Plot mean crater diameter (cm) against energy (J). Draw a smooth curve of best fit.

↑ Mean crater diameter (cm)Energy (J) →
  1. Describe the relationship shown by your graph.
  2. By what factor did the diameter increase when the energy increased eight times (0.10 m to 0.80 m)?
  3. Calculate the impact speed of the ball dropped from 1.20 m.
  4. Give two reasons why your crater is a poor model of a real impact crater.
Answers for the teacher
  1. For a 0.050 kg ball: Ep is 0.049 J at 0.10 m, 0.098 J at 0.20 m, 0.196 J at 0.40 m, 0.392 J at 0.80 m and 0.588 J at 1.20 m.
  2. The diameter increases as the energy increases, but less and less steeply: it is not proportional, and the curve flattens.
  3. Typically about 1.7 times, close to the fourth root of 8 (1.68).
  4. v = √(2gh) = √(2 × 9.8 × 1.20) = 4.8 m/s.
  5. Any two: real impacts are thousands of times faster (11 to 72 km/s on entering the atmosphere); real impactors and target rock melt and vaporise in an explosion-like release of energy; real craters form in solid rock, not loose sand; gravity and the size of the impactor are on completely different scales; the atmosphere slows or breaks up small impactors.

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