/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 \(\bullet$$\bullet\) Air-bag saf... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 17

\(\bullet$$\bullet\) Air-bag safety. According to safety standards for air bags, the maximum acceleration during a car crash should not exceed 60\(g\) and should last for no more than 36 ms. (a) In such a case, what force does the air bag exert on a 75 kg person? Start with a free-body diagram. (b) Express the force in part (a) in terms of the person's weight.

Short Answer

Expert verified
The airbag exerts a force of 44145 N, which is about 60 times the person's weight.

Step by step solution

01

Understanding the Problem

The problem involves computing the force exerted by an airbag on a 75 kg person during a car crash, where the maximum allowed acceleration is 60 times gravitational acceleration \(g\). You'll also need to express this force relative to the person's weight.
02

Free-Body Diagram Analysis

Imagine the free-body diagram for the person: The airbag exerts an upward force on the person during the crash to decelerate them. Assuming negligible other forces for simplicity, this force is the key to finding the answer.
03

Calculate the Force Using Maximum Acceleration

The acceleration involved is \(a = 60g\), where \(g = 9.81 \, \text{m/s}^2\). Use Newton's second law, \(F = ma\), where \(m = 75 \, \text{kg}\). Thus, the force \(F\) is given by:\[F = 75 \, \text{kg} \times 60 \times 9.81 \, \text{m/s}^2\]
04

Solve for Force

Substituting the values, compute the force:\[F = 75 \, \text{kg} \times 588.6 \, \text{m/s}^2 = 44145 \, \text{N}\]Thus, the airbag exerts a force of 44145 N on the person.
05

Express Force as a Multiple of Weight

The person's weight is given by \(W = mg = 75 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 735.75 \, \text{N}\). Now express the force as a multiple of this weight:\[\text{Force as multiple of weight} = \frac{44145}{735.75} \]
06

Calculate the Multiple

Divide the force by the weight to find the ratio:\[\frac{44145}{735.75} \approx 60\]The force is approximately 60 times the person's weight.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Airbag Safety Standards
Airbags are essential for car safety, designed to minimize injury during collisions. Safety standards set shared norms for their performance. The maximum acceleration that airbags should allow is 60 times the force of gravity. This is to ensure a rapid but controlled deceleration of the passengers. Such intense deceleration must last no longer than 36 milliseconds.
Having a standard like 60\(g\) (where \(g = 9.81 \, \text{m/s}^2\)) helps manufacturers design systems to cushion the passengers effectively. Airbags need to deploy swiftly but also safely to absorb crash forces without causing additional harm.
These standards aim to balance effective deceleration with minimizing risk to the human body, which can be vulnerable to rapid changes in speed.
Free-Body Diagram
A free-body diagram simplifies understanding of forces in physics problems. It is a visual tool to identify and represent all forces acting on an object.
In the context of an airbag during a crash, a free-body diagram for the person would typically include:
  • A force exerted upwards by the airbag, opposing the direction of motion.
  • Neglecting other forces allows focusing on this dominant force during the crash.
By isolating these forces, one can easily apply Newton's Second Law of Motion (\(F = ma\)). This helps calculate the force an airbag exerts to bring a passenger to a stop.
Force Calculation During Car Crash
Calculating the force experienced during a car crash involves understanding mass, acceleration, and Newton's Second Law. The law states that force equals mass times acceleration (\(F = ma\)).
Consider a 75 kg person experiencing acceleration of 60\(g\). Here, \(g\) is approximately \(9.81 \, \text{m/s}^2\), making the total acceleration \(60 \times 9.81\).
Plug these values into the equation:\[F = 75 \, \text{kg} \times 60 \times 9.81 \, \text{m/s}^2 = 44145 \, \text{N}.\]This calculates the force exerted by the airbag in newtons. For comparison, you can express this force as multiples of the person's weight, where weight \(W\) is \(m \times g = 735.75 \, \text{N}\). Thus, \[\text{Force as a multiple of weight} = \frac{44145}{735.75} \approx 60.\]This shows the airbag exerts a force 60 times the person's weight, illustrating how airbags manage extreme forces in crashes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\(\bullet$$\bullet\) A \(25.0-\mathrm{kg}\) box of textbooks rests on a loading ramp that makes an angle \(\alpha\) with the horizontal. The coefficient of kinetic friction is \(0.25,\) and the coefficient of static friction is 0.35 . (a) As the angle \(\alpha\) is increased, find the minimum angle at which the box starts to slip. (b) At this angle, find the accel- eration once the box has begun to move. (c) At this angle, how fast will the box be moving after it has slid 5.0 \(\mathrm{m}\) along the loading ramp"?

\(\bullet$$\bullet\) Force during a jump. An average person can reach a maximum height of about 60 \(\mathrm{cm}\) when jumping straight up from a crouched position. During the jump itself, the person's body from the knees up typically rises a distance of around 50 \(\mathrm{cm} .\) To keep the calculations simple and yet get a reason- able result, assume that the entire body rises this much during the jump. (a) With what initial speed does the person leave the ground to reach a height of 60 \(\mathrm{cm} ?\) (b) Make a free-body diagram of the person during the jump. (c) In terms of this jumper's weight \(W,\) what force does the ground exert on him or her during the jump?

\(\bullet$$\bullet\) You've attached a bungee cord to a wagon and are using it to pull your little sister while you take her for a jaunt. The bungee's unstretched length is \(1.3 \mathrm{m},\) and you happen to know that your little sister weighs 220 \(\mathrm{N}\) and the wagon weighs 75 \(\mathrm{N}\) . Crossing a street, you accelerate from rest to your normal walk- ing speed of 1.5 \(\mathrm{m} / \mathrm{s}\) in 2.0 \(\mathrm{s}\) , and you notice that while you're accelerating, the bungee's length increases to about 2.0 \(\mathrm{m}\) . What's the force constant of the bungee cord, assuming it obeys Hooke's law?

If the toboggan is well waxed so that there is no friction, what force does the sail have to provide to move the student-filled toboggan up the hill at a constant velocity (once it gets started)? \(\begin{array}{l}{\text { A. } g \sin \alpha} \\ {\text { B. } w \sin \alpha} \\\ {\text { C. } w} \\ {\text { D. } w g \sin \alpha}\end{array}\)

\(\bullet$$\bullet\) You are working for a shipping company. Your job is to stand at the bottom of an 8.0 -m-long ramp that is inclined at \(37^{\circ}\) above the horizontal. You grab packages off a conveyor belt and propel them up the ramp. The coefficient of kinetic friction between the packages and the ramp is \(\mu_{k}=0.30\) (a) What speed do you need to give a package at the bottom of the ramp so that it has zero speed at the top of the ramp? (b) Your coworker is supposed to grab the packages as they arrive at the top of the ramp, but she misses one and it slides back down. What is its speed when it returns to you?
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Electromagnetism

Read Explanation

Waves Physics

Read Explanation

Kinematics Physics

Read Explanation

Energy Physics

Read Explanation

Scientific Method Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.