Car bumpers are designed to limit the extent of damage to the car in the case of low-veloc...

Car bumpers are designed to limit the extent of damage to the car in the case of low-velocity collisions. Consider a 1420 kg passenger car impacting a concrete barrier while traveling at a speed of 5.0 km/h. Model the car as a particle and consider two bumper models: (1) a simple linear spring with constant k and (2) a linear spring of constant k in parallel with a shock absorbing unit generating a nearly constant force FS = 2000 N over 10 cm.

Figure P4.24

If the bumper is of type (1), find the value of k necessary to stop the car when the bumper is compressed 10 cm.