Newtons Cradle: Exploring Conservation of Energy and Momentum

In summary, the conversation discusses the concept of Newton's cradle and the question of why two balls on the opposite side cannot be moved with half the velocity of the first ball. The answer lies in the laws of conservation of energy and momentum, which would be violated if this were to happen. The conversation also includes a hint and explanation of how to set up the equations to show this violation.
  • #1
lennyp
4
0

Homework Statement


If one ball of a Newtons cradle is released at any velocity, why can't two balls on the other side be moved with half of the velocity of that ball.

Homework Equations


Law of consrvation of Energy and Low of conservation of Momentum


The Attempt at a Solution


Don't know where to start.
 
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  • #2
Well, suppose this does happen and set up equations of conservation of kinetic energy and conservation of momentum. We have the situation in which one ball moves with velocity v before the collision, with two at rest, then two balls move with velocity v/2 after the collision, with the first at rest. Try setting up the equations.
 
  • #3
Show how it violates Conservation of Energy
 
  • #4
Thanks for the hint but I don't understand how to plug in two objects on one side and one on the other side in the equation.
 
  • #5
Taking the expression for kinetic energy, note we are ignoring gravitational potential energy here since we are considering the velocity of the balls just after and before collision;

[tex]\underbrace{\frac{1}{2}mv^2}_{\text{First Ball}} = \underbrace{\frac{1}{2}mv'^2}_{\text{Second Ball}}+\underbrace{\frac{1}{2}mv'^2}_{\text{Third BallBall}}[/tex]

Now, all you need to do is plug in the value for [itex]v'[/itex], which is the velocity of the second two balls, and check the equality.
 
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1. How does Newton's Cradle demonstrate conservation of energy and momentum?

Newton's Cradle is a physical demonstration of the law of conservation of energy and momentum. When one ball is lifted and released to hit the others, the potential energy of the lifted ball is converted into kinetic energy as it falls and collides with the stationary balls. The energy is then transferred through the balls in a series of elastic collisions, demonstrating that the total energy remains constant.

2. What is the relationship between the number of balls and the speed of the Newton's Cradle?

The speed of the Newton's Cradle is directly proportional to the number of balls. This means that if you increase the number of balls, the speed of the cradle will also increase. This is because the more balls there are, the more energy is transferred through the elastic collisions, resulting in a faster movement of the balls.

3. Can the laws of conservation of energy and momentum be violated in Newton's Cradle?

No, the laws of conservation of energy and momentum cannot be violated in Newton's Cradle. This is because the amount of energy and momentum in the system always remains constant, regardless of the number of collisions or the speed of the balls. The cradle may appear to have a never-ending motion, but this is due to the conservation of energy and momentum rather than a violation of these laws.

4. How does the material of the balls affect the movement of Newton's Cradle?

The material of the balls can affect the movement of Newton's Cradle. Balls made of denser materials, such as metal, will transfer energy and momentum more efficiently, resulting in a longer-lasting movement of the cradle. On the other hand, balls made of less dense materials, such as plastic, may dissipate energy more quickly, resulting in a shorter movement of the cradle.

5. What other scientific principles can be demonstrated by Newton's Cradle?

Newton's Cradle can also demonstrate the principles of elastic and inelastic collisions, as well as the transfer of energy and momentum through a system. Additionally, it can be used to show the concept of impulse, which is the change in momentum caused by a force acting on an object. Furthermore, the cradle can be used to explain the concept of center of mass, as the balls move in a predictable pattern around the center of the cradle.

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