Answer:
a) F = - 6.75 10³ N, b) F = 1.35 10⁶ N
Explanation:
To calculate the force we can use the relation between the impulse and the moment
I = Δp
F t = m [tex]v_{f}[/tex] - m v₀
v_{f} = 0
F = -m v₀ / t
To calculate the time, let's use kinematics
a) Passenger with seat belt and airbag, braking distance x = 1 m
v² = v₀² - 2 a x
a = v₀² / 2x
a = 15²/2 1
a = 112.5 m / s²
v = v₀ - a t
t = v₀ / a
t = 15 / 112.5
t = 0.1333 s
Let's find the average strength
F = - 60 15 / 0.1333
F = -6750 N
F = -6.75 10³ N
b) Passenger without seat belt or airbag braking distance x = 5 mm = 0.005 m
a = v₀² / 2x
a = 15²/2 0.005
a = 22,500 m / s²
t = v₀ / a
t = 15/22500
t = 6.6667 10⁻⁴ s
The average strength is
F = - 60 15 / 6.6667 10⁻⁴
F = 1.35 10⁶ N