Motion & Force: Calculate Force from Car Collision w/ Abutment

[tjbateh]

Homework Statement

A car traveling at 48 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 53 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 40 kg?

Homework Equations

The Attempt at a Solution

Any idea how to solve this without using kinetic energy equations?

 

[tiny-tim]

… Any idea how to solve this without using kinetic energy equations?

Hi tjbateh!

You have an initial speed, a final speed, and a distance, so use one of the constant acceleration equations to find the acceleration …

then use F = ma.

 

[tomcue]

One way to approach this problem is by using Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, we can assume that the passenger's upper torso experiences a constant acceleration as it is brought to rest by the airbag. We can also assume that the direction of the acceleration is opposite to the direction of motion of the car.

We can use the equation F=ma, where F is the force, m is the mass, and a is the acceleration. We know the mass of the passenger's upper torso (40 kg) and we can calculate the acceleration using the distance traveled and the initial velocity of the car. Since the passenger moved 53 cm (0.53 m) and the car was traveling at 48 km/h (13.3 m/s), we can use the equation vf^2 = vi^2 + 2ad to solve for the acceleration. Plugging in the values, we get a = -50.2 m/s^2.

Now, we can plug in the values for mass and acceleration in the equation F=ma to calculate the force acting on the passenger's upper torso. This gives us a force of -2010 N. Note that the negative sign indicates that the force is acting in the opposite direction of motion, which makes sense as the airbag is slowing down the passenger's forward motion.

In summary, we can use Newton's Second Law and the equations for displacement and velocity to calculate the force acting on the passenger's upper torso during the car collision with the abutment.