Question

Automotive standards call for bumpers that sustain essentially no damage in a 4-km/h collision with a stationary object. As an automotive engineer, you'd like to improve on that. You've developed a spring-mounted bumper with effective spring constant 1.5 MN/m . The springs can compress up to 7.0 cm before damage occurs.

For a 1200-kg car. what do you claim as the maximum collision speed?

Answer 1

v = 8.90 km/h

Step-by-step explanation:

In order to calculate the maximum collision speed of the 1200kg car, you take into account that the the kinetic energy of the car when it has a speed v, is equal to the potential elastic energy of the spring when it is maximum compressed.

Then, you use the following equation:

`K=U\\\\(1)/(2)Mv^2=(1)/(2)kx^2` (1)

M: mass of the car = 1200kg

v: maximum collision speed of the car = ?

k: spring constant = 1.5MN/m = 1.5*10^6 N/m

x: maximum compression supported by the spring = 7.0cm = 0.070m

You solve the equation (1) for v and replace the values of the other parameters:

`v=x\sqrt{(k)/(M)}=(0.07m)\sqrt{(1.5*10^6N/m)/(1200kg)}\\\\v=2.47(m)/(s)`

In km/h you obtain:

`v=2.47(m)/(s)*(1km)/(1000m)*(3600s)/(1\ h)=8.90(km)/(h)`

The maximum collision that the car can support is 8.90km/h