Problem

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 P3.22

If the bumper is of type 1 and if k = 6500 lb/ft, find the spring compression necessary to stop the car.

Step-by-Step Solution

Solution 1

Step #1 of 5

Draw the free body diagram of the car.

$Y:\CF-TBS\21-1-15\New\4995-3-22P.jpg$

Step #2 of 5

Consider the equilibrium equations in x-direction.

…… (1)

Here, F is the spring force of the bumper, W is the weight of the car; g is the gravitational acceleration, and is the acceleration in the x-direction.