Question

What should the spring constant k of a spring be in order for it to bring a 1480 kg car to rest from a speed of 91.0 km/h such that the passengers undergo a maximum acceleration of 5g?

Answer 1

k = 5572 N/m

Step-by-step explanation:

Energy stored in the spring:

1)
`U=(1)/(2)kx^(2)`

Kinetic energy of the car:

2)
`K = (1)/(2)mv^(2)`

Spring force:

3)
`F_S=-kx`

Combining equation 1 and 2 and solving for k:

`(1)/(2)kx^(2)=(1)/(2)mv^(2)`

4)
`k = m((v)/(x))^(2)`

Using equation 3 and solve for x:

5)
`x=-(m)/(k)a`

Combining equation 4 and 5:

6)
`k=m(a^2)/(v^2)=25m(g^2)/(v^2)`