   Chapter 13, Problem 12P

Chapter
Section
Textbook Problem

An automobile having a mass of 1.00 × 103 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with constant 5.00 × 105 N/m and is compressed 3.16 cm as the car is brought to rest. What was the speed of the car before impact, assuming no energy is lost in the collision with the wall?

To determine
The speed of the automobile before impact.

Explanation

Given info: The mass of the automobile is 1.00×103Kg . The spring constant of the bumper is 5.00×106Nm-1 . The bumper is compressed 3.16 cm.

The total energy of the automobile at any point is given by,

E=Epot+Ekin

• E is the total energy
• Epot is the elastic potential energy
• Ekin is the kinetic energy of the block

Before impact the total energy is in the form of kinetic energy of the automobile and when it is stopped, the total energy is in the form of elastic potential energy. So according to the conservation of energy the potential energy

Epot(maxdis)=Ekin(equ)

• Epot(maxdis) is the elastic potential at the position of maximum displacement from the equilibrium position which is equal to 12kx02 where x0 is the maximum displacement.
• Ekin(equ) is the kinetic energy before impact which is equal to the 12mv02 where v0 is the velocity of the automobile before impact.

Hence,

12mv02=12kx02

On re-arranging,

v0=kx02m

Substitute 1

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