Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates 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.
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 air bag deploys.
Using the equation provided we can just substitute our knowns and solve for a.
(15m/s)^2=(0m/s)^2+2a(1m)
a=112.5 m/s^2
F=ma
F=(60kg)(112.5m/s^2)
6750 N
Rather wordy problem.
Vf^2=Vi^2+2ad
solve for a, then F=ma
Answers for Technology Trade-offs Quick Check
Seat belts are designed to be effective in(1 point)
The answer is: *speed collisions by applying a backward force on the body.*
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The right ans is : *Air bags can cause injury when they are too close to passengers, so manufacturers are still making improvements to the design.*
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the right answer is: *convenient fueling*
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The right answer is: *trading lower carbon dioxide emissions for lower up-front costs*
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ill get you 5/5:D
100% right
Thank you for the feedback and confirmation! I'm glad I could help.
To estimate the net force on the person during a head-on collision, we need to consider the two scenarios separately: when the person is wearing a seat belt and when the airbag deploys.
1. Seat Belt Scenario:
When a person wearing a seat belt is involved in a collision, the seat belt acts as a restraint by stretching and exerting a force on the person to slow them down gradually over a longer distance. In this case, the deceleration distance is about 1 m.
To estimate the force, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, since the person wearing the seat belt is decelerating over a distance, we can use the following equation:
F = m * a
The acceleration can be calculated using the equation of motion:
v^2 = u^2 + 2a*s
Where v is the final velocity (0 m/s since the person comes to a stop), u is the initial velocity (15 m/s), a is the acceleration, and s is the distance (1 m).
Solving for acceleration, we have:
a = (v^2 - u^2) / (2 * s)
Substituting the given values:
a = (0^2 - 15^2) / (2 * 1) = -225 / 2 = -112.5 m/s^2 (negative because it represents the deceleration)
Now, we can calculate the force:
F = m * a = 60 kg * (-112.5 m/s^2) = -6750 N
The negative sign indicates that the force is directed opposite to the initial motion, which is expected during deceleration.
2. Air Bag Scenario:
When an airbag deploys during a collision, it provides additional cushioning and absorbs some of the impact force on the person. The airbag inflates rapidly to create a larger surface area for the person to come into contact with, increasing the time over which the force is applied. This results in a lower overall force on the person.
It is difficult to estimate the exact force reduction provided by an airbag, as it depends on various factors such as the speed of deployment, size and position of the person, and the specific characteristics of the collision. However, studies have suggested that airbags can reduce forces exerted on the occupant by around 30% to 40%.
Assuming a conservative estimate of a 30% reduction in force, we can calculate the net force on the person with the airbag deployed:
Net force = Seat belt force - (Airbag force reduction * Seat belt force)
Net force = -6750 N - (0.3 * -6750 N) = -6750 N + 2025 N = -4725 N
Again, the negative sign indicates that the force is directed opposite to the initial motion.
So, in the scenario where a 60 kg person is in a head-on collision at 15 m/s with a seat belt and an airbag deploying, the estimated net force on the person would be approximately -4725 Newtons.