OwlSheets Students

Sizing Helmet Foam: Headform Mass, Impact Speed and Energy

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Sizing Helmet Foam: Headform Mass, Impact Speed and Energy

Use test lab data to see how mass and speed change kinetic energy.

Faster drops

Read the project notes and Table 1, then answer the questions.

Project Notes: How Much Energy Must the Foam Take?

1The bike-safety club at Halvorsen Middle School is designing a line of helmets for younger kids, teens and adults. Club members Marguerite Oyelaran and Dov Castellano are in charge of the foam liner, the thick layer inside the hard shell. In a crash, the foam crushes and takes up the head's kinetic energy, the energy it has because it is moving. Too little foam can crush all the way through; too much makes a helmet bulky and heavy. Their advisor, Ms. Rosalind Iwu, gave them the formula KE = ½ × m × v², with the mass m in kilograms (kg), the speed v in meters per second (m/s) and the energy in joules (J).

2To see real tests, the club visited a helmet test lab. Technician Mr. Anatole Ferrante explained that the lab straps a helmet onto a headform, a metal model of a human head, and drops it onto a steel block called an anvil. Headforms come in several sizes, and the bigger sizes have more mass. In many bicycle helmet tests, the helmet hits the anvil at roughly 5 to 6 m/s. Mr. Ferrante raises or lowers the drop height to set the speed at impact, and a sensor reads that speed.

3For the club, Mr. Ferrante ran a demonstration while the students watched from behind a clear safety shield. He fixed a flat pad of liner foam, with no helmet shell, on top of the anvil and dropped the 5.0 kg headform onto it at three speeds. He used a fresh pad of the same foam for every drop and measured how deep the dent was afterward (Table 1).

4He also showed the energy his software calculated for four headform sizes at an impact speed of 4.0 m/s (bar graph).

5Back at school, the club looked at three foam liners. Liner A is the thinnest and lightest, and it can safely take up to 60 J. Liner B can take up to 100 J. Liner C is the thickest and heaviest, and it can take up to 140 J. Marguerite proposed a rule: each helmet gets the lightest liner that can take the kinetic energy of its test.

Table 1: 5.0 kg Headform Dropped on Foam Pads
Impact speed (m/s)	Kinetic energy (J)	Dent in foam (mm)
2.0	10	2
4.0	40	8
6.0	?	18

1.

Use the formula in paragraph 1 to find the missing value in Table 1.

At 6.0 m/s, the 5.0 kg headform had J of kinetic energy.

2.

Use Table 1. The impact speed of 6.0 m/s is 3 times the impact speed of 2.0 m/s.

The dent from the 6.0 m/s drop was times as deep as the dent from the 2.0 m/s drop.

3.

Marguerite says, "Going from 4.0 m/s to 6.0 m/s is only 2 m/s faster, the same step as going from 2.0 m/s to 4.0 m/s. So it should add about the same energy." Which evidence from Table 1 shows that her idea is wrong?

A. The same 5.0 kg headform was used for the three speeds, so its mass did not change.B. Each 2 m/s step deepened the dent by about the same 6 mm, so the two energy steps were equal.C. The step from 2.0 to 4.0 m/s deepened the dent by 6 mm, but the next step deepened it by 10 mm.D. The step from 2.0 to 4.0 m/s added 30 J, but the next step added less energy than that.

4.

Why did Mr. Ferrante use the same 5.0 kg headform and a fresh pad of the same foam for every drop in Table 1?

A. So that the headform would gain more mass as it fell from higher upB. So that a change in the dent comes from the speed, not the mass or the foamC. So that the headform would hit the anvil at the same speed on each of the dropsD. So that each drop would make a dent of the same depth in the foam

Bigger heads and the liner choice

Use the bar graph, Table 1 and paragraph 5 to answer the questions.

5.

Use the bar graph. Compare the 6.0 kg headform with the 3.0 kg headform.

At the same speed, the 6.0 kg headform had times the kinetic energy of the 3.0 kg headform.

6.

Which statement best describes the bar graph?

A. The energy rose by the same 8 J for each extra kilogram of headform mass.B. Doubling the mass from 3.0 kg to 6.0 kg made the energy 4 times as large.C. The heavier headforms had less energy, since they moved more slowly at impact.D. The energy rose by a larger amount for each kilogram, like the speed pattern in Table 1.

7.

In Table 1 the dent grew in step with the kinetic energy. Suppose that pattern holds for every headform, and the 6.0 kg headform hits a fresh foam pad at 4.0 m/s. Use the bar graph and Table 1. Do not round.

The dent would be about mm deep.

8.

Use Marguerite's rule in paragraph 5. Find the kinetic energy of each test, then sort each test by the lightest liner that can take it.

9.

Dov says, "For the adult helmet we should worry about bigger heads more than faster crashes. Starting from the 5.0 kg headform at 6.0 m/s, going up to a 6.0 kg headform adds more energy than going up to 7.0 m/s." Do you agree? Write a claim, support it with calculations or data from the table and the graph, and explain your reasoning about how mass and speed each affect kinetic energy.