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Chapter 7: Problem 16

Using momentum and force principles, explain why an air bag reduces injury in an automobile collision.

Short Answer

Expert verified
Answer: An air bag helps reduce injury to passengers during a car collision by slowing down the rate of change of their momentum and distributing the force experienced over a larger area and time. This lessens the impact of the collision, effectively reducing the risk of severe injuries.

Step by step solution

01

Understand the concepts of momentum and force

Momentum is the product of an object's mass and velocity (p = mv), which is a measure of the object's motion. Force (F) acting on an object is related to the rate of change of its momentum with respect to time, as given by Newton's second law of motion: F = dp/dt. In a car collision, the car and its passengers experience a sudden change in velocity. Their momentum changes rapidly, which results in a large force acting on the passengers.
02

Consider the relation between momentum and force during a collision

During a collision, the passengers' momentum changes from an initial value to zero, as the vehicle comes to a sudden stop. This change in momentum occurs over a short period of time. The force on the passengers can be calculated as the rate of change in momentum over this short time span. Without any safety measures, the force experienced by the passengers would be extremely high due to the quick change of momentum. The passengers' bodies would experience strong impact forces, leading to a higher risk of injury.
03

Understand the purpose of the air bag

The main function of an air bag is to slow down the change in momentum of the passengers, thereby reducing the force experienced by them. When a collision occurs, the air bag inflates rapidly, providing a cushion between the passenger and the vehicle's hard surfaces. As the passengers come in contact with the air bag, their body will be decelerated over a longer length of time as they are pushed against the air bag. The extended duration of deceleration will reduce the overall force experienced by the passengers, minimizing the risk of injury.
04

Analyze the effect of the air bag on the force experienced by the passengers

By slowing down the rate of change of momentum, the air bag effectively reduces the force acting on the passengers. Using Newton's second law (F = dp/dt), we can see that, by increasing the time it takes for the passengers' momentum to change, the force experienced by them is decreased. Hence, the air bag acts as a force-distributing mechanism, spreading the force experienced by the passengers over a larger area and time, which lessens the impact of the collision and reduces the likelihood of injury. In conclusion, the air bag works on the principles of momentum and force to protect passengers during automobile collisions. By slowing down the rate of change of momentum and distributing the force experienced by the passengers, it effectively reduces the risk of severe injuries.

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Most popular questions from this chapter

Cosmic rays from space that strike Earth contain some charged particles with energies billions of times higher than any that can be produced in the biggest accelerator. One model that was proposed to account for these particles is shown schematically in the figure. Two very strong sources of magnetic fields move toward each other and repeatedly reflect the charged particles trapped between them. (These magnetic field sources can be approximated as infinitely heavy walls from which charged particles get reflected elastically.) The high- energy particles that strike the Earth would have been reflected a large number of times to attain the observed energies. An analogous case with only a few reflections demonstrates this effect. Suppose a particle has an initial velocity of \(-2.21 \mathrm{~km} / \mathrm{s}\) (moving in the negative \(x\) -direction, to the left), the left wall moves with a velocity of \(1.01 \mathrm{~km} / \mathrm{s}\) to the right, and the right wall moves with a velocity of \(2.51 \mathrm{~km} / \mathrm{s}\) to the left. What is the velocity of the particle after six collisions with the left wall and five collisions with the right wall?

Current measurements and cosmological theories suggest that only about \(4 \%\) of the total mass of the universe is composed of ordinary matter. About \(22 \%\) of the mass is composed of dark matter, which does not emit or reflect light and can only be observed through its gravitational interaction with its surroundings (see Chapter 12). Suppose a galaxy with mass \(M_{\mathrm{G}}\) is moving in a straight line in the \(x\) -direction. After it interacts with an invisible clump of dark matter with mass \(M_{\mathrm{DM}}\), the galaxy moves with \(50 \%\) of its initial speed in a straight line in a direction that is rotated by an angle \(\theta\) from its initial velocity. Assume that initial and final velocities are given for positions where the galaxy is very far from the clump of dark matter, that the gravitational attraction can be neglected at those positions, and that the dark matter is initially at rest. Determine \(M_{\mathrm{DM}}\) in terms of \(M_{\mathrm{G}}, v_{0},\) and \(\theta\).

A 3.0 -kg ball of clay with a speed of \(21 \mathrm{~m} / \mathrm{s}\) is thrown against a wall and sticks to the wall. What is the magnitude of the impulse exerted on the ball?

Rank the following objects from highest to lowest in terms of momentum and from highest to lowest in terms of energy. a) an asteroid with mass \(10^{6} \mathrm{~kg}\) and speed \(500 \mathrm{~m} / \mathrm{s}\) b) a high-speed train with a mass of \(180,000 \mathrm{~kg}\) and a speed of \(300 \mathrm{~km} / \mathrm{h}\) c) a 120 -kg linebacker with a speed of \(10 \mathrm{~m} / \mathrm{s}\) d) a 10 -kg cannonball with a speed of \(120 \mathrm{~m} / \mathrm{s}\) e) a proton with a mass of \(6 \cdot 10^{-27} \mathrm{~kg}\) and a speed of \(2 \cdot 10^{8} \mathrm{~m} / \mathrm{s}\).

Two balls of equal mass collide and stick together as shown in the figure. The initial velocity of ball \(\mathrm{B}\) is twice that of ball A. a) Calculate the angle above the horizontal of the motion of mass \(\mathrm{A}+\mathrm{B}\) after the collision. b) What is the ratio of the final velocity of the mass \(A+B\) to the initial velocity of ball \(A, v_{f} / v_{A} ?\) c) What is the ratio of the final energy of the system to the initial energy of the system, \(E_{\mathrm{f}} / E_{\mathrm{i}}\) ? Is the collision elastic or inelastic?
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