Question

A 72.5-kg person is riding in a car moving at 20.5 m/s (assume this is the positive direction) when the car runs into a bridge abutment. This problem will illustrate why the invention of the airbag dramatically improved the safety of automobiles. show answer Incorrect Answer 50% Part (a) Calculate the horizontal component of the average force, in newtons, on the person if he is stopped by a padded dashboard that compresses an average of 1.15 cm.Calculate the horizontal component of the average force, in newtons, on the person if he is stopped by an air bag that compresses an average of 13.5 cm

Answer 1

Explanation:

Given that,

Mass of the person, m = 72.5 kg

Initial speed of the car, u = 20.5 m/s

(a) Let $F_x$ is the horizontal component of the average force, in newtons, on the person if he is stopped by a padded dashboard that compresses an average of 1.15 cm, x = 0.0115 m and v = 0

Using the second law of motion to find it as:

$F_x=m\times a$

Using the third equation of kinematics to find a.

$F_x=m\times \dfrac{v^2-u^2}{2s}$

$F_x=-m\times \dfrac{u^2}{2s}$

$F_x=-72.5\times \dfrac{(20.5)^2}{2\times 0.0115}$

$F_x=-1.32\times 10^6\ N$

(b) Here, x = 13.5 cm = 0.135 m

$F_x=-m\times \dfrac{u^2}{2s}$

$F_x=-72.5\times \dfrac{(20.5)^2}{2\times 0.135}$

$F_x=-1.12\times 10^5\ N$

Hence, this is the required solution.

Answer 2

Answer:

A)  f_{dashboard} = 1324701 N

B)  f_{airbag} = 112844.90 N

Explanation:

Given data:

mass of person = 72.5 kg

velocity of person = 20.5 m/s

we know that from newton's 2nd law

f = ma

$f = m \frac{v^2 - u^2}{2s}$

final velocity is v = 0

$f = - \frac{mu^2}{2s}$

$f = \frac{72.5\times 20.5^2}{2\times 1.15\times 10^{-2}}$

f = 1324701 N

B)

$f_{airbag} = f = \frac{72.5\times 20.5^2}{2\times 1.3.5\times 10^{-2}}$

$f_{airbag} = 112844.90 N$