# Today's cars have elastic bumpers that are designed to compress and rebound without any physical...

## Question:

Today's cars have elastic bumpers that are designed to compress and rebound without any physical damage at speeds below about 5 mi/h (8 km/h). The material of the bumpers behaves essentially as an ideal spring up to that point but permanently deforms beyond that. If the compression corresponding to the elastic limit for a particular bumper is 1.5 cm, what must be the effective spring constant of the bumper material, assuming the car has a mass of 1150 kg and is tested by ramming into a solid wall?

## Spring Energy:

An object oscillating on the end of a spring will move back and forth, sometimes moving and sometimes momentarily at rest. So, the object's kinetic energy changes with time. By conservation of energy, this kinetic energy must change form and be stored somewhere. It is stored as potential energy in the spring, when the spring is compressed or stretched.

The spring potential energy of an object depends on the spring constant {eq}k {/eq} and the displacement from equilibrium {eq}x {/eq}:

{eq}U = \frac{1}{2}kx^2 {/eq}

## Answer and Explanation:

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Let's consider the energy of this situation before and after the collision.

Initially, we have a car moving forward with kinetic energy. There is no...

See full answer below.

#### Learn more about this topic: Hooke's Law & the Spring Constant: Definition & Equation

from

Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.