/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 25 In a totally inelastic collision... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 25

In a totally inelastic collision between two equal masses, with one initially at rest, show that half the initial kinetic energy is lost.

Short Answer

Expert verified
Half of the initial kinetic energy is indeed lost in a completely inelastic collision between two equal masses, where one starts of being at rest. This is justified by our calculations which compares the initial and final kinetic energies, finding a factor of 2. This indicates a loss of half of the initial kinetic energy.

Step by step solution

01

Set Up the Initial Conditions

Let the two masses be \( m_1 \) and \( m_2 \), both of equal mass \( m \). Let \( m_1 \) be in motion with initial speed \( u \), and \( m_2 \) be at rest, i.e., \( u_2 = 0 \). The total initial kinetic energy (\( KE_{initial} \)) is given by \( KE_{initial} = \frac{1}{2} m_1 u^2 + \frac{1}{2} m_2 u_2^2 = \frac{1}{2} m u^2 \), since \( m_2 \) is at rest.
02

Denote Final Conditions

In a totally inelastic collision, the two masses stick together and move as a single object after the collision. Let \( v \) be the final velocity of the combined mass. Since the momentum is conserved in the collision, we can express \( v \) using the initial momentum: \( m_1*u_1 + m_2*u_2 = (m_1 + m_2)*v \), which simplifies to \( m * u = 2*m * v \), and finally to \( v = \frac{1}{2} u \).
03

Compute the Final Kinetic Energy

The total final kinetic energy (\( KE_{final} \)) after they stick together is given by \( KE_{final} = \frac{1}{2} (m_1 + m_2) v^2 = \frac{1}{2} * 2m * (\frac{1}{2}u)^2 = \frac{1}{8} m u^2 \).
04

Compare Initial and Final Kinetic Energy

Comparing the initial kinetic energy with the final kinetic energy, it is discovered that the final energy is half of the initial energy. This can be seen by dividing the initial by the final which gives a factor of 2, hence half the initial kinetic energy is lost.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A \(55-\mathrm{g}\) firecracker is at rest at the origin when it explodes into three pieces. The first, with mass \(7 \mathrm{~g}\), moves along the \(x\)-axis at \(33 \mathrm{~m} / \mathrm{s}\). The second, with mass \(15 \mathrm{~g}\), moves along the \(\mathrm{y}\)-axis at 26 \(\mathrm{m} / \mathrm{s}\). Find the velocity of the third piece.

A thin rod extends from \(x=0\) to \(x=L\). It carries a nonuniform mass per unit length \(\mu=M x^{a} / L^{1+a}\), where \(M\) is a constant with units of mass, and \(a\) is a non-negative dimensionless constant. Find expressions for (a) the rod's mass and (b) the location of its center of mass. (c) Are your results what you expect when \(a=0 ?\)

Three \(200-\mathrm{g}\) objects have velocities given by \(\vec{v}_{1}=15.0 \hat{j} \mathrm{~m} / \mathrm{s}\), \(\vec{v}_{2}=6.7 \hat{i}-3.45 \hat{j} \mathrm{~m} / \mathrm{s}\), and \(\vec{v}_{3}=-6.7 \hat{i}-4.32 \hat{j} \mathrm{~m} / \mathrm{s}\). Find the kinetic energy of the center of mass and the internal kinetic energy of this system.

A block of mass \(m\) undergoes a one-dimensional elastic collision with a block of mass \(M\) initially at rest. If both blocks have the same speed after colliding, how are their masses related?

Find an expression for the center of mass of a solid hemisphere, given as the distance from the center of the flat part of the hemisphere.
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Kinematics Physics

Read Explanation

Electrostatics

Read Explanation

Electricity and Magnetism

Read Explanation

Fluids

Read Explanation

Medical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.