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 3300 lb passenger car impacting a concrete barrier while traveling at a speed of 4.0 mph. Model the car as a particle, and consider two types of bumper: (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 of 700 lb over 0.25 ft.

Figure P3.23

If the bumper is of type 1, find the value of k necessary to stop the car when the bumper is precompressed 0.25 ft.