Companion to the reading passage The Fastest Man on Earth: Physics of Crash Survival. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
In 1954, Air Force researcher John Paul Stapp rode a rocket-powered sled to test how much deceleration a restrained human body can survive. Rockets accelerated the sled along a straight, level track. The sled then entered a water brake that brought it to rest. Instruments on the sled recorded its speed and acceleration throughout the run. Table 1 lists values for the run. During the braking phase, the instruments showed that the deceleration was not constant: it rose to a single brief maximum and was much smaller during most of the stop.
Table 1: Stapp’s 1954 Rocket Sled Run
| Quantity | Value |
|---|---|
| Mass of Stapp | 76.2 kg |
| Maximum speed of sled | 282.5 m/s |
| Time to reach maximum speed from rest | 5.0 s |
| Time to stop from maximum speed (braking phase) | 1.4 s |
| Peak (maximum) deceleration recorded during braking | 452.8 m/s2 (46.2 times g) |
Values are rounded from published accounts of the run; some records list a slightly shorter stopping time.
1. Which mathematical representation can be used to determine the magnitude of the average net force on Stapp during the braking phase?
2. An engineer makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
When the water brake slowed the sled, Stapp’s body tended to keep moving forward. A multi-point harness attached to the seat pressed against his chest, shoulders, and waist. During braking, the sled was moving toward the right of the page and slowing down. Throughout the stop, Stapp remained seated upright with the seat supporting him from below.
3. You are drawing a free-body diagram of Stapp (a dot) during the braking phase. First, the force of the harness on Stapp: choose its direction (the sled moves toward the right of the page) and use Table 1 to determine its average magnitude. Assume the harness provides the entire horizontal force on Stapp.
4. Now complete the free-body diagram. Place a check mark in three boxes to indicate statements that describe a correct free-body diagram of Stapp during the braking phase, with arrow lengths showing relative sizes.
5. Which row correctly describes the force of the harness on Stapp and the force of Stapp on the harness during the braking phase? (Force of harness on Stapp / Force of Stapp on harness)
Stapp’s results helped convince automakers to test restraint systems. Engineers used a crash-test dummy with a mass of 70 kg in a car traveling at 27 m/s that struck a rigid barrier. They measured how long it took the dummy to come to rest for three different restraint conditions. In every test the dummy’s speed went from 27 m/s to 0 m/s. The results are shown in Table 2.
Table 2: Stopping Time of a 70-kg Dummy (initial speed 27 m/s)
| Restraint Condition | Time for Dummy to Stop (s) |
|---|---|
| No restraint (dummy strikes dashboard) | 0.010 |
| Seat belt only | 0.10 |
| Seat belt and air bag | 0.15 |
Data are representative values for practice.
6. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the average force on the dummy in the seat belt and air bag test. Then calculate the force.
7. An engineer proposes making the front of the car much stiffer so that it crumples less during a crash. Explain one disadvantage of this design for the occupant, in terms of the occupant’s stopping time and the average force on the occupant.