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Chapter 1: Problem 4

In severe head-on automobile accidents, a deceleration of \(60 \mathrm{~g}\) 's or more \(\left(1 \mathrm{~g}=9.81 \mathrm{~m} / \mathrm{s}^{2}\right)\) often results in a fatality. What force, in \(\mathrm{N}\), acts on a child whose mass is \(22.7 \mathrm{~kg}\), when subjected to a deceleration of \(60 \mathrm{~g}\) 's?

Short Answer

Expert verified
The force acting on the child is 13,357.62 N.

Step by step solution

01

- Understand the problem

You need to find the force acting on a child with a given mass when subjected to a specific deceleration. The deceleration is given in terms of 'g'.
02

- Convert the deceleration to \(\mathrm{m/s^2}\)

Since \(1 \mathrm{~g} = 9.81 \mathrm{~m/s^2}\), a deceleration of \(60 \mathrm{~g}\) is \(60 \times 9.81 \mathrm{~m/s^2} = 588.6 \mathrm{~m/s^2}\)
03

- Use Newton's Second Law

Newton's Second Law states that \(F = ma \). Here, \( F \) is the force, \( m \) is the mass of the child (\(22.7 \mathrm{~kg}\)), and \( a \) is the deceleration (\(588.6 \mathrm{~m/s^2}\)).
04

- Calculate the force

Using the formula \(F = ma \), substitute the given values: \( F = 22.7 \times 588.6 = 13,357.62 \mathrm{~N} \)

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Key Concepts

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

Deceleration
Deceleration is a term used to describe a decrease in the speed of an object. It represents negative acceleration, meaning the object's velocity is reducing over time. In the context of severe automobile accidents, deceleration measures how quickly a vehicle comes to a stop.
Here鈥檚 how to break it down:
  • Deceleration is given in 'g' units, where 1 g = 9.81 m/s虏.
  • A deceleration of 60 g implies the object slows down at a rate of 60 times 9.81 m/s虏, resulting in 588.6 m/s虏.
Understanding deceleration helps you gauge the severity of a crash and the force the passengers experience during such events.
Force Calculation
When calculating force in physics, Newton's Second Law is your go-to formula. This law states:
\( F = ma \)
  • \( F \) represents the force in Newtons (N).
  • \( m \) is the mass of the object in kilograms (kg).
  • \( a \) stands for acceleration or deceleration in meters per second squared (m/s虏).
Let's apply this to our problem:
Given mass \( m \) = 22.7 kg and deceleration \( a \) = 588.6 m/s虏,
You substitute the values into the formula:
\[ F = 22.7 \times 588.6 = 13,357.62 \mathrm{~N} \]
This calculation reveals that the force acting on the child during the accident is 13,357.62 N.
Mass and Acceleration
Mass and acceleration are key factors in understanding force.
  • Mass (m) measures the amount of matter in an object and is always constant irrespective of location.
  • In our problem, the child's mass is given as 22.7 kg.
Acceleration (or deceleration) measures how quickly an object鈥檚 speed changes. It varies based on the forces acting on the object.

Deceleration in our problem was a hefty 60 g, converted to 588.6 m/s虏 for easier use in calculations. Understanding how mass and acceleration interrelate through Newton's Second Law helps highlight how even small masses can generate significant forces under high acceleration or deceleration, such as in a car crash.

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Most popular questions from this chapter

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