Question

A set of crash tests consists of running a test car moving at a speed of 12.6 m/s (27.7 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 63.0 kg (138.6 lbs) dummy is found to move a distance of 0.720 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.

The force that acts on the dummy has to do (negative) work on the dummy. It must slow the dummy and stop it. Thus the amount of work equals the kinetic energy of the dummy. From the equation of work done by a force we can calculate that force. Using the direction of motion as positive direction, calculate the average acceleration of the dummy during that time (in g's) (use 1g=9.8 m/s2).

Use Newton's second law. What should the sign of the answer be? The dummy is being slowed down, so the acceleration is - since the dummy is moving in the + direction. In a different car, the distance the dummy moves while being stopped is reduced from 0.720 m to 0.210 m calculate the average force on the dummy as that car stops.

Answer 1

Given data:

Mass of the dummy is m = 63.0 kg

Initial speed of the car is v₀ = 12.6m/s

The distance moved by dummy during the collision is x = 0.720 m

The change in kinetic energy of the car is,

             

                                  

From work energy theorem, the change in kinetic energy is equal to work done.

           

Thus, the average force is,

Apply Newton's second law of motion to find the average acceleration.

         

          

In terms of "g":

        

When the distance has reduced to 0.720 m to 0.210 m, then acceleration of the car is,

         

           

According to Newton's second law the average force on dummy in different car,

         F = ma