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Colt1911 [192]
3 years ago
7

Suppose you want to design an air bag system that can protect the driver at a speed 100 km/h (60 mph) if the car hits a brick wa

ll.
Estimate how fast the air bag must inflate to effectively protect the driver. How does the use of a seat belt help the driver?
Physics
1 answer:
34kurt3 years ago
3 0

When solving question that contains equations and the use mathematical computations, It is always ideal to list the parameters given.

Now, given that:

  • the speed of the car which is the initial velocity (u) = 100 km/h before it hits the wall.
  • after hitting the wall, the final velocity will be (v) = 0 km/h

Assumptions:

  • Suppose we make an assumption that the distance travelled during the collision of the car with the brick wall (S) = 1 m
  • That the car's acceleration is also constant.

∴

For a motion under constant acceleration, we can apply the kinematic equation:

\mathsf{v^2 = u^2 + 2as}

where;

v = final velocity

u = initial velocity

a = acceleration

s = distance

From the above equation, making acceleration (a) the subject of the formula:

\mathsf{v^2 - u^2 =2as }

\mathsf{a = \dfrac{v^2 - u^2 }{2s}}

The initial velocity (u) is given in km/h, and we need to convert it to m/s as it has an effect on the unit of the acceleration.

since 1 km/h = 0.2778 m/s

100 km/h = 27.78 m/s

\mathsf{a = \dfrac{(0)^2 - (27.78)^2 }{2(1)}}

\mathsf{a = \dfrac{- 771.7284 }{2}}

a = - 385.86 m/s²

Similarly, from the kinematic equation of motion, the formula showing the relation between time, acceleration and velocity is;

v = u + at

where;

v = 0

-u = at

\mathsf{t = \dfrac{-u}{a}}

\mathsf{t = \dfrac{-27.78}{-385.86}}

t = 0.07 seconds

An airbag is designed in such a way as to prevent the driver from hitting on the steering wheel or other hard substance that could damage the part of the body. The use of the seat belt is to keep the driver in shape and in a balanced position against the expansion that occurred by the airbag during the collision on the brick wall.

Thus, we can conclude that the airbag must be inflated at 0.07 seconds faster before the collision to effectively protect the driver.

Learn more about the kinematic equation here:

brainly.com/question/11298125?referrer=searchResults

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Friction always acts____ and in the ____ direction of the motion of an object ​
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Answer:

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A student measures the speed of sound by echo destiny classes hands and then measures the time to hear the echo his distance to
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A 3.0-kg block starts at rest at the top of a 37° incline, which is 5.0 m long. Its speed when it reaches the bottom is 2.0 m/s.
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Answer: f_{r} = 16.49N

Explanation: The object is placed on an inclined plane at an angle of 37° thus making it weight have two component,

W_{x} = horizontal component of the weight = mgsinФ

W_{y} = vertical component of weight = mgcosФ

Due to the way the object is positioned, the horizontal component of force will accelerate the object thus acting as an applied force.

by using newton's law of motion, we have that

mgsinФ - f_{r} = ma

where m = mass of object=5kg

a = acceleration= unknown

Ф = angle of inclination = 37°

g = acceleration due to gravity = 9.8m/s^{2}

f_{r} = frictional force = unknown

we need to first get the acceleration before the frictional force which is gotten by using the equation below

v^{2} = u^{2} + 2aS

where v = final velocity = 2m/s

u = initial velocity = 0m/s (because the object started from rest)

a= unknown

S= distance covered = length of plane = 5m

2^{2} = 0^{2} + 2*a*5\\\\4= 10 *a\\\\a = \frac{4}{10} \\a = 0.4m/s^{2}

we slot in a into the equation below to get frictional force

mgsinФ - f_{r} = ma

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17.9633 - f_{r} =  1.2

f_{r} = 17.9633 - 1.2

f_{r} = 16.49N

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3 years ago
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