during a collision, a driver of mass m in a car moving at speed v is brought to rest by an inflated air bag in time t. (a) write an equation showing the average force the air bag exerts on the driver. (b) suppose the mass of the driver is 55 kg, the initial speed of the car is 28 m/s, and the contact time with the air bag is 0.20 s. show that the average age force is 7700 N.
momentum change = m v
force = rate of change of momentum
= m v/t
55 * 28/.2 = 7700
To find the average force exerted by the airbag on the driver during the collision, we can use Newton's second law of motion, which states that the force applied to an object is equal to the rate of change of its momentum. Mathematically, this can be expressed as:
Force = (Change in momentum) / (Time)
(a) Let's denote the initial momentum of the driver as p₁, the final momentum as p₂, and the average force as F. The change in momentum (∆p) can be calculated as:
∆p = p₂ - p₁
Since the driver is brought to rest, the final momentum of the driver (p₂) is zero. Therefore, ∆p = -p₁.
Substituting this into the equation:
Force = (∆p) / (Time)
Force = -p₁ / t
(b) Now, let's substitute the given values into the equation. The mass of the driver is m = 55 kg, the initial speed of the car is v = 28 m/s, and the contact time with the airbag is t = 0.20 s.
The initial momentum of the driver (p₁) can be calculated using the equation:
p₁ = m * v
Substituting the values:
p₁ = 55 kg * 28 m/s
p₁ = 1540 kg·m/s
Now, we can find the average force (F) using the equation:
Force = -p₁ / t
Substituting the values:
Force = -1540 kg·m/s / 0.20 s
Force = -7700 N
Since the force is negative, it indicates that the airbag applies a force in the opposite direction of the car's motion, helping to bring the driver to a stop.
Therefore, the average force exerted by the airbag on the driver during the collision is 7700 N.