Car bumpers are designed to limit the extent of damage to the car in the case of

Question

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/hr, as shown in Figure 3. 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 with a shock absorbing

unit generating a near constant force Fs=2000 N over 10 cm.

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

bumper is compressed 10 cm.

b. If the bumper is of type (2), find the value of k necessary to stop the car when the

bumper is compressed 10 cm.

Explanation / Answer

The KE of the car is 0.5*1420*(5*5/18)^2 J = 1369.59 J 10 cm = 0.1m the work done by compressing 10 cm of the spring should be equal to the KE of the car. work done by the spring is 0.5*k*x^2= .005k where x = .1m equating with the 1st eqn I get .005k = 1369.59 J so k = 273919 N/m ans (a) in the 2 nd case the car has a force absorbing unit which dies work equivalent to 2000*.1J = 200J so work done by the spring = 1369.59-200J=1169.59J so .005k = 1169.59 J k = 233918N/m ans (b)

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