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Deceleration is sometimes measured in \(g\) 's or multiples of the standard acceleration of gravity. Determine the force, in newtons, that an automobile passenger whose mass is \(68 \mathrm{~kg}\) experiences if the deceleration in a head-on crash is \(50 \mathrm{~g}\).

Short Answer

Expert verified
The force that a passenger whose mass is \(68 \mathrm{~kg}\) experiences if the deceleration in a head-on crash is \(50 \mathrm{~g}\) is \(33354 \mathrm{N}\).

Step by step solution

01

Convert g to m/s^2

Because g is the standard acceleration due to gravity, we will begin by recalling the value of g, which is approximately \(9.81 \mathrm{m/s}^2\). We multiply this by the given deceleration in g's to convert it to m/s^2. Therefore, our deceleration is \(50g = 50* 9.81 \mathrm{m/s}^2 = 490.5 \mathrm{m/s}^2\). Note that we changed our sign as deceleration is negative acceleration.
02

Apply Newton’s second law of motion

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. Mathematically it is defined as \(F = ma\). Given that the mass (m) is \(68 \mathrm{~kg}\) and the deceleration/acceleration (a) is \(490.5 \mathrm{m/s}^2\), plug these values into the equation to calculate the force.
03

Calculate the Force

Using the established values from previous steps, the force \(F\) can be calculated as follows: \(F = ma = 68 \mathrm{~kg} * 490.5 \mathrm{m/s}^2 = 33354 \mathrm{N}\).

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Key Concepts

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

Deceleration and g-forces
When we talk about deceleration in physics, we're referring to the process of slowing down. It's the opposite of acceleration, and can be quite hazardous, especially when it happens rapidly, such as during car accidents. In these contexts, deceleration is often measured in 'g-forces' (g). One g is the acceleration due to Earth's gravity, which is roughly equal to \(9.81 \text{m/s}^2\).

Experiencing high g-forces can have significant effects on the body; for instance, in a head-on car crash, the sudden deceleration can cause the body to experience forces multiple times their own weight. These forces are a measure of the stress that can potentially lead to injuries. Understanding these forces is crucial for designing safety features in vehicles, like seat belts and airbags, to protect passengers during extreme deceleration events.
Newton's second law of motion
Moving objects abide by the rules of motion, and one of the most fundamental rules is Newton's second law. It tells us that the force applied to an object produces an acceleration proportional to the force and inversely proportional to the object's mass. In mathematical terms, this is expressed as \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration.

When an object slows down, this law is still applicable. The deceleration is considered a negative acceleration. For safety analysis, such as automotive crash scenarios, Newton's second law helps us assess the force exerted on passengers, which is crucial for understanding the potential harm a person could suffer in the event of deceleration.
Conversion of units
Physics calculations often involve different units of measurement, and converting between these units is essential for accurate results. When dealing with forces and motions, we typically measure acceleration in meters per second squared (\(\text{m/s}^2\)) and force in newtons (N), with the mass in kilograms (kg).

Understanding how to convert from one unit to another, such as from g-forces to \(\text{m/s}^2\), is essential, especially in practical applications like engineering and physics. Proper conversions ensure that quantities like force can be accurately calculated and understood within the appropriate context, such as safety testing or vehicle design.
Calculating force
Calculating the force experienced by an object or individual involves using Newton's second law and the proper conversion of units. Once you understand the mass of the object and the acceleration (or deceleration, in the case of a car crash), you can determine the force involved. In the example of an automobile carrier, we first convert the deceleration from g-forces to \(\text{m/s}^2\) and then apply the formula \(F = ma\) to find the force in newtons.

This calculation offers valuable insights into the stresses endured by objects or individuals during rapid changes in velocity. It is not only applicable in traffic accident analysis but also in numerous other scenarios, such as the design of roller coasters or space shuttle launches, where understanding the force can help guarantee safety and functionality.

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