A human has a reasonable chance of surviving an automobile crash if the body's deceleration is no more than 30 "g's". (1 "g" is 9.8 m/s^2) Calculate the force the body would have withstand decelerating at this rate. What is the distance travelled if the car was initially travelling at 90 km/hr?
F=ma
then, for the last part...
vf^2= vo^2 + 2a * d where a= -30g
solve for d.
To calculate the force experienced by the body during deceleration, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
First, let's convert the acceleration from "g's" to meters per second squared:
1 "g" = 9.8 m/s^2
So, the acceleration is 30 "g's" * 9.8 m/s^2/g = 294 m/s^2.
Next, we need to convert the initial velocity from km/hr to m/s:
1 km/hr = 1000 m / 3600 s = 0.2778 m/s
Therefore, the initial velocity is 90 km/hr * 0.2778 m/s = 25 m/s.
Now, we can calculate the deceleration force:
F = m * a
Since we don't have the mass of the body mentioned in the question, we cannot provide the exact force. However, assuming a standard mass of 70 kg for an average adult, let's calculate the force in that case:
F = 70 kg * 294 m/s^2
F ≈ 20,580 N (Newtons)
Keep in mind that this is an approximation, and the actual force can vary depending on the mass of the person involved in the crash.
Moving on to the distance travelled during deceleration, we need to use the formula for linear motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity, which is 0 m/s because the car comes to a stop.
- u is the initial velocity, which is 25 m/s.
- a is the deceleration, which is -294 m/s^2 (negative as it opposes the motion).
- s is the distance we want to calculate.
Plugging in the values, we can solve for s:
0^2 = (25 m/s)^2 + 2(-294 m/s^2) * s
0 = 625 m^2/s^2 - 588 m/s^2 * s
588 m/s^2 * s = 625 m^2/s^2
s = 625 m^2/s^2 / 588 m/s^2
s ≈ 1.063 m
Therefore, the approximate distance travelled by the car during deceleration is 1.063 meters.