Air bags are designed to deploy in 10 ms. Estimate the acceleration of the front surface of the ba as it expands. Express your answer in terms of the acceleration of gravity g.
To estimate the acceleration of the front surface of the airbag as it expands, we can use a simple kinematic equation:
vf = vi + at
Where:
vf = final velocity = 0 m/s (since the airbag starts at rest)
vi = initial velocity = unknown
a = acceleration = unknown
t = time = 10 ms = 0.01 s
We can assume that the acceleration is constant during this short time period.
Solving for acceleration, we can rearrange the equation as:
a = (vf - vi) / t
Since the final velocity is 0 m/s, the equation simplifies to:
a = -vi / t
Now, we can substitute the acceleration due to gravity, g, for the initial velocity, vi:
a = -g / t
Plugging in the values, we have:
a = -g / 0.01
Simplifying:
a = -100g
Hence, the acceleration of the front surface of the airbag as it expands is -100 times the acceleration due to gravity, g.
To estimate the acceleration of the front surface of the airbag as it expands, we can use the formula for acceleration:
acceleration = change in velocity / time
In this case, the change in velocity is the velocity of the front surface of the airbag when it expands, and the time is the deployment time of 10 ms (or 0.01 seconds).
Since the airbag is designed to deploy rapidly, we can assume it starts from rest and reaches its final velocity in the given time. Thus, we can approximate the change in velocity as:
change in velocity = final velocity - initial velocity
Considering that the initial velocity is 0 m/s, we can simplify the equation to:
change in velocity = final velocity
Now, using the formula for average velocity, we can express the final velocity as:
final velocity = (initial velocity + final velocity) / 2
Since the airbag starts from rest, the initial velocity is 0 m/s. Rearranging the equation, we have:
2 * final velocity = final velocity
Simplifying further, we find:
final velocity = 0 m/s
Now, we can substitute the values into the acceleration formula:
acceleration = change in velocity / time
= final velocity / time
= 0 m/s / 0.01 seconds
= 0 m/s²
Therefore, the estimated acceleration of the front surface of the airbag as it expands is 0 m/s².
figure it goes .3 m in 10m/s
average velocity=.3/.001
final velocity= twice that.
acceleration= final veloicity/.001
or acceleration= .6/.001g= 600/9.8= 60 g