Seatbelts provide two main advantages in a car accident: (i) they keep you from being thrown from the car, and (ii) they reduce the force that acts on you during the collision to survivable levels. The second benefit can be illustrated by comparing the net force exerted on the driver of a car in a head-on collision with and without a seatbelt.

Question

Seatbelts provide two main advantages in a car accident: (i) they keep you from being thrown from the car, and (ii) they reduce the force that acts on you during the collision to survivable levels. The second benefit can be illustrated by comparing the net force exerted on the driver of a car in a head-on collision with and without a seatbelt. 
(a) A driver wearing a seatbelt decelerates at the same rate as the car itself. Since modern cars have a "crumple zone" built into the front of the car, the car will decelerate over a distance of roughly 1.0 m. Find the net force acting on a 62 kg driver who is decelerated from 19 m/s to rest in a distance of 1.0 m. 
? kN

(b) A driver who does not wear a seatbelt continues to move forward with a speed of 19 m/s (due to inertia) until something solid is encountered. The driver now comes to rest in a much shorter distance -- perhaps only a centimeter. Find the net force acting on a 62 kg driver who is decelerated from 19 m/s to rest in 1.0 cm. 
? kN 
I am not sure how to set this problem up. Can someone describe the picture or suggest which equations to use?

a) 
avg force *distance= 1/2 mass*initialvelocity^2

b) same formula, distance has changed.

Bot · Answer

a) We can calculate the net force acting on the driver using the work-energy theorem, which states that work done on an object is equal to its change in kinetic energy:

avg force * distance = 1/2 * mass * initial_velocity^2

We are given the initial velocity (19 m/s), mass of the driver (62 kg), and the distance over which the car decelerates (1 m). Plugging these values into the equation, we get:

avg force * 1.0 m = 1/2 * 62 kg * (19 m/s)^2

avg force = (1/2 * 62 kg * 361 m^2/s^2) / 1.0 m

avg force = 11221 kg m/s^2

To convert this force into kN, we divide the value by 1000:

avg force = 11.22 kN

Thus, the net force acting on the driver is 11.22 kN.

b) We use the same formula as in part (a), but now the distance over which the driver decelerates is only 1.0 cm or 0.01 m. Plugging this value into the equation, we get:

avg force * 0.01 m = 1/2 * 62 kg * (19 m/s)^2

avg force = (1/2 * 62 kg * 361 m^2/s^2) / 0.01 m

avg force = 1122100 kg m/s^2

To convert this force into kN, we divide the value by 1000:

avg force = 1122.1 kN

Thus, the net force acting on the driver is 1122.1 kN.