(Solved): Required information Car bumpers are designed to limit the extent of damage to the car in the case ...

Required information Car bumpers are designed to limit the extent of damage to the car in the case of low-velocity collisions. Consider a 3000 Ib passenger car impacting a concrete barrier while traveling at a speed of $$4.0\mathrm{mph}$$. Model the car as a particle, and consider two types of bumpers: (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 $$700\mathrm{lb}$$ over $$0.25\mathrm{ft}$$. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. If the bumper is of type 2 , find the value of $$k$$ necessary to stop the car when the bumper is compressed $$0.25\mathrm{ft}$$. (Round the final answer to four decimal places.) The value of $$k$$ necessary to stop the car is $$\times 10^4\mathrm{lb}/\mathrm{ft}$$.