BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Solutions

Chapter
Section
BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

To temporarily increase the bodys water content, a person need only. a. consume extra salt. b. consume extra su...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

Give the molecular formula for each of the following structural formulas.

General Chemistry - Standalone book (MindTap Course List)

All the human senses have ___. (1.3)

An Introduction to Physical Science

Look Figure 1.6. How can you tell that Mercury does not follow a circular orbit?

Horizons: Exploring the Universe (MindTap Course List)