Question

An automobile of mass 2000 kg is driven into a brick wall in a safety test. The bumper behaves like a Hooke’s-law spring. It has an effective spring constant of 4 × 106 N/m, and is observed to compress a distance of 1.39 cm as the car is brought to rest. What was the initial speed of the automobile? Answer in units of m/s.

Answer 1

Answer:0.621 m/s

Step-by-step explanation:

Given

mass of automobile
`m=2000 kg`

Effective spring constant
`k=4* 10^6 N/m`

compression in spring
`x=1.39 cm`

Conserving Energy i.e. Kinetic energy of automobile=Elastic potential Energy of spring

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

`(2000\cdot v^2)/(2)=(4* 10^6* (1.39* 10^(-2))^2)/(2)`

`v^2=(4* 1.39^2* 10^2)/(2000)`

`v=0.621 m/s`