A car traveling at 58 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 63 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of 43 kg?
Impulse (force*time) equals momentum change.
Initial velocity Vo = 16.11 m/s
Average velocity while stopping = Vo/2 = 8.055 m/s
Initial momentum of torso = 693 kg*m/s
Time to stop = 0.63 m/Vaverage
= 0.078 s
Average force = (momentum change)/time
= 693/0.078 = ___ N
To find the magnitude of force acting on the passenger's upper torso, we can use Newton's second law of motion, which states that force (F) is equal to the product of mass (m) and acceleration (a): F = m * a.
First, we need to find the acceleration experienced by the passenger. We know that the passenger moves forward a distance of 63 cm (or 0.63 meters) while being brought to rest by the airbag.
Acceleration can be calculated using the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. In this case, the final velocity is 0 m/s (since the passenger is brought to rest), the initial velocity is the velocity of the car (58 km/h), and the displacement is 0.63 meters.
Converting the initial velocity to meters per second:
58 km/h = 58,000 meters/3,600 seconds = 16.11 m/s.
Plugging the values into the equation:
0^2 = (16.11)^2 + 2a * 0.63.
Simplifying the equation:
259.92 + 1.26a = 0.
Now, we can solve for the acceleration (a):
1.26a = -259.92.
a = -259.92 / 1.26 = -206.22 m/s^2.
Note: The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
Finally, we can substitute the mass of the passenger (43 kg) and the calculated acceleration (-206.22 m/s^2) into Newton's second law to find the magnitude of force:
F = m * a = 43 kg * (-206.22 m/s^2) = -8,871.66 N.
Thus, the magnitude of force acting on the passenger's upper torso is approximately 8,871.66 N.