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CP BIO Whiplash Injuries. When a car is hit from behind,

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 69P Chapter 6

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 69P

CP BIO Whiplash Injuries.? When a car is hit from behind, its passengers undergo sudden forward acceleration, which can cause a severe neck injury known as ?whiplash?. During normal acceleration, the neck muscles play a large role in accelerating the head so that the bones are not injured. But during a very sudden acceleration, the muscles do not react immediately because they are flexible; most of the accelerating force is provided by the neck bones. Experiments have shown that these bones will fracture if they absorb more than 8.0 J of energy. (a) If a car waiting at a stoplight is rear-ended in a collision that lasts for 10.0 ms, what is the greatest speed this car and its driver can reach without breaking neck bones if the driver’s head has a mass of 5.0 kg (which is about right for a 70-kg person)? Express your answer in m/s and in mi/h. (b) What is the acceleration of the passengers during the collision in part (a), and how large a force is acting to accelerate their heads? Express the acceleration in m/s2 and in g’s.

Step-by-Step Solution:

Solution 69P Step 1: a) The initial velocity of the person, u = 0 m/s The final velocity of the person, v = Mass of the head, m = 5 kg Maximum energy with which the bones can withstand, E = 8.0 J Therefore, we can write, the change in Kinetic energy during the collision, KE = 8.0 J That is, ½ mv - ½ mu = 8.0 J Or, ½ mv - 0 = 8.0 J v = 2 × 8.0 J / m = 16 J / 5 kg = 3.2 m /s 2 2 Taking square roots on both sides, v = 1.79 m/s 1 mile = 1609.34 m Therefore, 1 m = 1/1609.34 miles 1 hour = 3600 s 1 s = 1/3600 h Changing the units, v = 1.79 {(1/1609.34 )/(1/3600)} mi/hr v = 1.79 (3600/1609.34) mi/hr = 1.79 × 2.24 mi/hr = 4 mi/hr Step 2: b) rovided, the time for the collision, t = 10 ms 1 ms = 10 s-3 10 ms = 10×1 0 s = 10 s2 Take the initial velocity of the car, u = 1.79 m/s Final velocity of the car, v = 0 m/s (it comes to rest after the collision) v = u+at (Newton’s equations of motion) Substituting the values in the equation, -2 0 = 1.79 m/s + (a × 10 s) -2 - 1.79 m/s = (a × 10 s) Rearranging the equation, a = - 1.79 m/s / 10 s -2 a = - 179 m/s . this is the acceleration (deceleration) experienced by the passenger.

Step 3 of 3

Chapter 6, Problem 69P is Solved
Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

Since the solution to 69P from 6 chapter was answered, more than 326 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: University Physics, edition: 13. The answer to “CP BIO Whiplash Injuries.? When a car is hit from behind, its passengers undergo sudden forward acceleration, which can cause a severe neck injury known as ?whiplash?. During normal acceleration, the neck muscles play a large role in accelerating the head so that the bones are not injured. But during a very sudden acceleration, the muscles do not react immediately because they are flexible; most of the accelerating force is provided by the neck bones. Experiments have shown that these bones will fracture if they absorb more than 8.0 J of energy. (a) If a car waiting at a stoplight is rear-ended in a collision that lasts for 10.0 ms, what is the greatest speed this car and its driver can reach without breaking neck bones if the driver’s head has a mass of 5.0 kg (which is about right for a 70-kg person)? Express your answer in m/s and in mi/h. (b) What is the acceleration of the passengers during the collision in part (a), and how large a force is acting to accelerate their heads? Express the acceleration in m/s2 and in g’s.” is broken down into a number of easy to follow steps, and 185 words. This full solution covers the following key subjects: acceleration, bones, neck, during, Car. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 69P from chapter: 6 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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