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The human body can survive a negative acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than . If you are in an automobile accident with an initial speed of and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

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Ciara Beatrice Canalita
Ciara Beatrice CanalitaLv10
18 Jun 2019
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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Seat belts and airbags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1m as the front of the car crumples. An occupant restrained by seat belts and airbags decelerate with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm.

Part A.
A 60 kg person is in a head-on collision. The car's speed at impact is 15 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the airbag deploys.

Part B.
Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or airbag.

Part C
What is the force in part A in terms of the person's weight?

Part D
What is the force in part B in terms of the person's weight?

2. An inflatable bag is located in the dashboard of a car. Inacollision, the bag expands suddenly and cushions the impact ofthepassenger. The forward motion of the passenger must be stoppedinabout 30 cm of motion if contact with the hard surfaces of thecaris to be avoided.
a) For a 70-kg person with a 30-cm allowed stopping distance,showthat the magnitude of the average force is given by thefollowingexpression: F = 117 Vo^2, newtons.
Notice that the necessary stopping force increases as the squareofthe velocity of the automobile (and the passenger).
b) Assume that Vo = 70 km/h and find F.
c) If the force that you evaluated in part b) isuniformlydistributed over a 1000-cm^2 area of the passenger's body,find theapplied force per square meter. The estimated strength ofbodytissue is 500,000 Pa. NOTE: One Pa (Pascal) is a force of 1Ndivided by one area of 1 square meter.
d) Kindly, repeat the calculation of part c) with v = 100 km/h.Itis safe to say that the force per unit area just calculatedwouldprobably injure the passenger?

To demonstrate the tremendous acceleration of a top fuel dragracer, you attempt to run your car into the back of a dragster thatis "burning out" at the red light before the start of a race.(Burning out means spinning the tires at high speed to heat thetread and make the rubber sticky.)

You drive at a constant speed of toward the stopped dragster, notslowing down in the face of the imminent collision. The dragsterdriver sees you coming but waits until the last instant to put downthe hammer, accelerating from the starting line at constantacceleration, . Let the time at which the dragster starts toaccelerate be .

a- What is , the longest time after the dragster begins toaccelerate that you can possibly run into the back of the dragsterif you continue at your initial velocity?

b- Assuming that the dragster has started at the last instantpossible (so your front bumper almost hits the rear of the dragsterat ), find your distance from the dragster when he started. If youcalculate positions on the way to this solution, choose coordinatesso that the position of the drag car is 0 at . Remember that youare solving for a distance (which is a magnitude, and can never benegative), not a position (which can be negative).

c- Find numerical values for and in seconds and meters for the(reasonable) values (26.8 m/s) and .
Separate your two numerical answers by commas, and give your answerto two significant figures.

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