Companion to the reading passage The Physics of 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.
A seat belt retractor normally lets the belt slide in and out freely. To lock the belt in a crash, many retractors use an inertia sensor. In Model 1, a small steel ball rests in a shallow cup fixed to the car’s frame. A lever sits on top of the ball. When the ball rolls up the side of the cup, it lifts the lever into the teeth of a gear on the belt spool, and the spool can no longer turn. During normal driving at constant velocity, the ball stays at the bottom of the cup.
1. The car is moving forward and the driver brakes hard. Which statement best explains why the ball rolls toward the front of the cup?
A belt that locks completely rigid can stop the occupant very quickly. Many modern belts include a torsion bar, a metal rod that twists at a set load and lets out a few centimeters of belt. Engineers compared a rigid belt with a load-limiting belt in sled tests. A 75-kg crash-test dummy slowed from 15 m/s to 0 m/s in each test. Table 1 shows the time each dummy took to stop and how far the dummy’s chest moved forward while stopping.
Table 1: Sled Tests of Two Belt Designs (75-kg dummy, 15 m/s to 0 m/s)
| Belt Design | Time for Dummy to Stop (s) | Forward Distance Moved by Chest While Stopping (m) |
|---|---|---|
| Rigid belt | 0.060 | 0.45 |
| Load-limiting belt | 0.090 | 0.68 |
Data are representative values for practice.
2. Which mathematical representation can be used to determine the magnitude of the average force on the dummy wearing the load-limiting belt?
3. An engineer makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
4. Based on Table 1, describe one trade-off engineers must consider when deciding how much belt the torsion bar should let out.
Passengers often leave slack in their belts. With slack, the occupant keeps moving forward for a moment after the car begins to slow, and the belt then catches the occupant suddenly. A pre-tensioner removes the slack a few milliseconds before impact so the belt holds the occupant snugly against the seat from the start. Consider an occupant whose speed decreases from the same initial value to zero in both cases. During the crash, the car is moving toward the right of the page and slowing down.
5. Free-body diagram of the belted occupant while the car (moving to the right) slows down. Assume the occupant is the 75-kg dummy wearing the load-limiting belt from Table 1 (15 m/s to 0 in 0.090 s). Choose the direction of the force of the belt on the occupant and determine its average magnitude.
6. Same occupant (75 kg). The gravitational force Fg points down. Choose the direction of the force of the seat on the occupant and determine its magnitude.
7. Which row correctly compares an occupant whose belt has slack with an occupant whose belt was pulled snug by a pre-tensioner?
(Change in momentum of occupant with slack / Time for occupant with slack to stop / Average force on occupant with slack)