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Module 2

1. Module 2

1.11. Page 2

Physics 30 Module 2 Lesson 2

Module 2—The Conservation of Momentum in Isolated Systems

Explore

 

A two-sequence image shows two positions in a Newton’s cradle, a pendulum device with seven silver balls in a row, each suspended by two strings that are attached to opposite sides of the top of a frame. The first position shows the ball at the left end of the row in motion, away from the row of balls and swinging toward it. The second position shows the left ball stationary in the row of balls and the ball at the right end of the row swinging forward away from the rest.

© KUCO/shutterstock

A two-sequence image shows two positions in a Newton’s cradle, a pendulum device with seven silver balls in a row, each suspended by two strings that are attached to opposite sides of the top of a frame. The first position shows the ball at the left end of the row in motion, away from the row of balls and swinging toward it. The second position shows the left ball stationary in the row of balls and the ball at the right end of the row swinging forward away from the rest.

© KUCO/shutterstock


 

Have you ever played with a device like this? It’s called Newton’s cradle. Spend a few moments playing with this animation of Newton’s cradle.

 

As you are playing, see if you can answer these questions:

  • What happens if you change the number of balls put into motion?


  • Do you ever get a different number of balls leaving the pack than enters it?

  • How does the velocity of the entering balls compare to the velocity of the leaving balls?

  • Notice the height at which the balls start their swing toward the pack. How does that initial height compare to the final height the balls reach when they swing away from the pack?

During your play with the animation, you surely saw that momentum was conserved. One ball enters and one ball leaves, and the velocities are basically the same. The same was true for two balls or even three. Momentum would have been conserved if one ball entered and two balls left with half the velocity of the original ball. Did that ever happen? (Knowing how the applet works makes the answer to that question an emphatic no!)

 

The answer to the last of the questions gives you a clue to what is happening. For example, you may have used just one starting ball. Since the starting height of the ball and the ending height of the ball seem to be the same, the energy seems to have been conserved. Just before impact, the energy of the moving ball can be calculated. You’ll remember the equation, . Just after the collision, the new moving ball will have the same kinetic energy. (These concepts would still be true if you had used more than one starting ball.) Kinetic energy appears to be conserved in Newton's cradle, but is kinetic energy always conserved in collisions?

 

DID YOU KNOW?

The units for energy are joules (J), named after James Prescott Joule. The joule is not a base SI unit but is made of other SI units.

 

 

 

Is Kinetic Energy Conserved in a Collision?

 

Some of the energy in a closed, isolated system is in the form of kinetic energy. This is particularly true for two objects that collide, since one or both must be moving in order for this to occur.

 

Self-Check

 

SC 1.Two bumper cars, each with a mass of 50 kg and travelling at 0.75 m/s, are headed straight toward each other.

  1. What is the momentum of each car? Do the cars have the same momentum? (Remember: Momentum is a vector quantity.)

  2. What is the total momentum of the system?

  3. What is the kinetic energy of each car? Do the cars have the same kinetic energy?  (Remember: Kinetic energy is a scalar quantity.)

  4. What is the total kinetic energy of the system?

Check your work.
Self-Check Answers

 

SC 1.

 

a.           


   Each car has a different momentum. They are identical in magnitude but opposite in direction.

 

b.

 

   The total momentum of the system is zero.

 

c.

 

   Both cars have the same kinetic energy because it is a scalar quantity.

 

d.

 

   The total kinetic energy of the system is 28 J.