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FREE ONLINE Knowing where our textbooks are used can help us provide better services to students and receive more grant support for future projects. Significance Notice that after the collision, the blue puck is moving to the right; its direction of motion was reversed. This Open Stax book is available for free at Chapter 9 | Linear Momentum and Collisions 437 9.7 Check Your Understanding There is a second solution to the system of equations solved in this example (because the energy equation is quadratic): v 1,f = −2.5 m/s, v 2,f = 0 .

If you’re using an Open Stax textbook, either as required for your course or just as an extra resource, send your course syllabus to [email protected]and you’ll be entered to win an i Pad Mini. This solution is unacceptable on physical grounds; what’s wrong with it? Iron Man The 2012 movie “The Avengers” has a scene where Iron Man and Thor fight.

The point of all this is that, in analyzing a collision or explosion, you can use both momentum and kinetic energy. Write down the expression for conservation of momentum. If kinetic energy is conserved, write down the expression for conservation of kinetic energy; if not, write down the expression for the change of kinetic energy. You now have two equations in two unknowns, which you solve by standard methods.

In this case, the total kinetic energy of the system is conserved. In any interaction of a closed system of objects, the total momentum of the system is conserved ( → p f= → p i) but the kinetic energy may not be: • If 0 K i , the interaction is an explosion.

Since the objects are all motionless after the collision, the final kinetic energy is also zero; the loss of kinetic energy is a maximum.

However, it turns out again that, although the total momentum of the system of objects remains constant, the kinetic energy doesn’t; but this time, the kinetic energy decreases. In the extreme case, multiple objects collide, stick together, and remain motionless after the collision.

The total mass of this composite object is the sum of the masses of the original objects, and the new single object moves with a velocity dictated by the conservation of momentum.

This interaction—one object becoming many, with an increase of kinetic energy of the system—is called an explosion. In the case of gunpowder burning and pushing out a bullet, chemical potential energy is converted to kinetic energy of the bullet, and of the recoiling gun.

Many-to-Many The extreme case on the other end is if two or more objects approach each other, collide, and bounce off each other, moving away from each other at the same relative speed at which they approached each other.

Such a collision is said to be perfectly inelastic.

Through our partnerships with companies and foundations committed to reducing costs for students, Open Stax is working to improve access to higher education for all. Thus, kinetic energy is not conserved, but momentum is.

Open Stax CNX The technology platform supporting Open Stax is Open Stax CNX ( one of the world’s first and largest open-education projects. Thus, we use conservation of energy to determine the final velocity of the system.

Gates Sr., under the direction of Bill and Melinda Gates and Warren Buffett. Solution Conservation of momentum, in this case, reads pi = pf m 2 v 2,i = m 1 v 1,f m 2 v 2,f .