Question

A 67.0 kg person is riding in a car moving at 19.0 m/s when the car runs into a bridge abutment. (Assume the initial velocity is in the positive direction.) (a) Calculate the average force (in N) on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. (Indicate the direction with the sign of your answer.) N (b) Calculate the average force (in N) on the person if he is stopped by an air bag that compresses an average of 15.0 cm. (Indicate the direction with the sign of your answer.) N

Answer 1

a) F = - 1.21 10⁶ N, b) F = - 8.06 10⁴ N

Step-by-step explanation:

a) For this part let's use the kinematics relations

v² = v₀² - 2 a x

distance traveled to stop is x = 1.00 cm = 0.0100 cm, final speed is zero

0 = v₀² - 2 ax

a = v₀² / 2x

a =
`(19^2 )/(2 \ 0.01)`

a = 1.81 10⁴ m / s²

this acceleration is in the opposite direction to velocity

let's use Newton's second law

F = ma

F = 67.0 (-1.81 10⁴)

F = - 1.21 10⁶ N

the negative sign indicates that it is going in the opposite direction to the speed

b) in this case it is stopped by an airbag x = 15.0 cm = 0.15 m

a = v₀² / 2x

a =
`(19^2)/(2 \ 0.15)`

a = 1.203 10³ m / s²

calculate the force

F = m a

F = 67.0 (- 1.203 10³)

F = - 8.06 10⁴ N