A 60kg front seat passenger in a car moving initially with a speed of 18m/s (40 MPH) is brought to rest by an air bag in a time of 0.4s
a. What is the impulse acting on the passenger?
b.What is the average force acting on the passenger in this process?
40 Miles/hr is actually 17.88 m/s, not 18, but let's say it's 18.
The initial momentum, is 60*18 = 1080 kg m/s.
That equals the impulse and the momentum change hen stopping.
Divide the impulse by the time (in seconds) for the average force, in newtons.
Fav = 1080/0.4 = ___ N
2700
To solve this problem, we can use the impulse-momentum theorem, which states that the impulse acting on an object is equal to the change in momentum of the object.
a. To find the impulse acting on the passenger, we can use the formula:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
The initial momentum of the passenger is:
Initial momentum = mass × initial velocity
Plugging in the values:
Initial momentum = 60 kg × 18 m/s
Next, we need to find the final momentum. Since the passenger is brought to rest, the final velocity is 0 m/s. So, the final momentum is:
Final momentum = mass × final velocity
Final momentum = 60 kg × 0 m/s = 0 kg m/s
Using the formula for impulse:
Impulse = Final momentum - Initial momentum
Impulse = 0 kg m/s - (60 kg × 18 m/s)
Impulse = -1080 N s
So, the impulse acting on the passenger is -1080 N s.
b. To find the average force acting on the passenger, we use the formula:
Average force = Impulse / Time
Plugging in the values:
Average force = -1080 N s / 0.4 s
Average force = -2700 N
The negative sign indicates that the force is acting in the opposite direction of the motion.
Therefore, the average force acting on the passenger is -2700 N.
To find the impulse acting on the passenger, we can use the impulse-momentum principle, which states that the impulse acting on an object is equal to the change in momentum of that object. The formula for impulse is:
Impulse = Change in momentum
Impulse = Mass * Change in velocity
a. First, let's find the change in velocity of the passenger. Since the passenger was brought to rest, their final velocity is 0 m/s.
Change in velocity = Final velocity - Initial velocity
Change in velocity = 0 m/s - 18 m/s
Change in velocity = -18 m/s
Now we can calculate the impulse:
Impulse = Mass * Change in velocity
Impulse = 60 kg * (-18 m/s)
Impulse = -1080 kg⋅m/s
Therefore, the impulse acting on the passenger is -1080 kg⋅m/s.
b. To find the average force acting on the passenger, we can use the formula for average force:
Average force = Impulse / Time
Since we already calculated the impulse to be -1080 kg⋅m/s, we just need to divide it by the given time of 0.4 seconds:
Average force = -1080 kg⋅m/s / 0.4 s
Average force = -2700 N
Therefore, the average force acting on the passenger in this process is -2700 Newtons. The negative sign indicates that the force is acting in the opposite direction of the initial velocity.