Effect of Varying Ball Size in Newton's Cradle

  • Thread starter d4rr3n
  • Start date
In summary, a Newtons cradle is a device where the ball at one end moves with similar velocity to the other balls, minus the gradual slowing due to energy loss. If the size/mass of the balls gradually decrease, the smaller ball will move with a greater velocity than the larger ball due to the mass ratio. It is not necessary to have a great number of balls, but there is a minimum number required for the same velocity difference. The motion will not be periodic like in an equal-mass cradle, but interesting patterns can be created with specific mass ratios. When the large ball is lifted and released, its kinetic energy will be transmitted through the decreasing size balls, causing the last ball to accelerate away from the others with a
  • #1
d4rr3n
53
0
In a Newtons cradle the ball at one end of the ball train moves with similar velocity to the other minus the gradual slowing due to loss of energy in both.

What would be the result if I made a Newtons cradle in which the size/mass of the balls gradually decrease?
My instinct tells me that the small ball will move with several times grater velocity then the large ball but not sure why. Also assuming that assertion in correct is it necessary to have a great number of balls of different sizes, what is the minimum number that would result in the same velocity difference?
 
Physics news on Phys.org
  • #2
If the large ball was lifted and released, when it struct the others, all would tend to spread out.
If the small one was lifted and release, it would bounce off, and again, the balls would tend to spread.
In general, the motion would not become periodic as it is with the equal-mass cradle. But you could probably find mass ratios for the balls that would create interesting periodic patterns.
 
  • #3
If the large ball was lifted and released would not its kinetic energy be transmitted through the decreasing size balls causing the last to accelerate away from the others with a grater velocity then the large ball that initiated the process?
 
  • #4
d4rr3n said:
If the large ball was lifted and released would not its kinetic energy be transmitted through the decreasing size balls causing the last to accelerate away from the others with a grater velocity then the large ball that initiated the process?
Let's say that the masses were 4, 2, 1.
4 hits 2 with velocity 1.
-- The average velocity is reduce by the mass increase by (4/6) to 0.667, but they will still recede from each other at v=1.
-- So 4 moves forward at 0.667-0.333 = 0.333.
-- 2 moves forward at 0.667 + 0.667 = 1.333.
2 immediately hits 1 with velocity 1.333
-- The average velocity is reduced by the mass increase by (2/3) to 0.8889, but they will still recede from each other at v=1.333.
-- So 2 moves forward at 0.8889-0.4444 = 0.4444. This is still faster that the 4 ball, so there is no further collision.
-- 1 moves away at 0.88889+0.88889 = 1.77778.

So immediately after 4 strikes 1 and 2 all move forward: 4 at 0.333; 2 at 0.444; and 1 at 1.778.
 
  • #5
In a Newtons cradle when one ball strikes one end only the last moves forward, the force is merely transmitted through the others...but you are saying they will all move forward? In the example you gave I would expect 4 to strike 2 and 1 to rapidly accelerate away from 2, I would expect 2 to hardly move but merely act as a path of the kinetic energy.
 

1. How does an asymmetrical Newton's cradle work?

An asymmetrical Newton's cradle works by utilizing the principles of Newton's laws of motion. The balls on one side are lifted to a certain height and released, causing them to transfer their energy to the balls on the opposite side. This transfer of energy creates a chain reaction and causes the last ball to swing out.

2. What is the difference between a regular Newton's cradle and an asymmetrical one?

The main difference between a regular Newton's cradle and an asymmetrical one is the size and weight of the balls. In an asymmetrical cradle, the balls on one side are larger and heavier than the ones on the other side. This difference in weight creates an imbalance and allows for the transfer of energy to occur.

3. Can you explain the conservation of momentum in an asymmetrical Newton's cradle?

The conservation of momentum in an asymmetrical Newton's cradle refers to the fact that the total momentum of the system remains constant. When the balls on one side are released, they transfer their momentum to the balls on the opposite side, causing them to move. This transfer of momentum continues until it reaches the last ball, which then swings out with the same momentum as the first ball.

4. How does the angle of release affect the movement of the balls in an asymmetrical Newton's cradle?

The angle of release can affect the movement of the balls in an asymmetrical Newton's cradle. If the balls are released at a steeper angle, they will have more potential energy and will transfer more energy to the balls on the opposite side. This can cause the last ball to swing out with more force. On the other hand, if the balls are released at a shallower angle, they will have less potential energy and the transfer of energy will be less dramatic.

5. What are some real-world applications of an asymmetrical Newton's cradle?

An asymmetrical Newton's cradle can be used as a visual aid to demonstrate the principles of conservation of momentum and energy transfer. It is also commonly used as a desk toy or educational tool. In addition, the concept of an asymmetrical cradle has been applied in the design of certain engines and machines to transfer energy efficiently.

Similar threads

  • Mechanics
2
Replies
53
Views
2K
Replies
1
Views
1K
Replies
4
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
78
  • STEM Educators and Teaching
Replies
4
Views
3K
Replies
2
Views
1K
  • Mechanics
Replies
17
Views
4K
  • Introductory Physics Homework Help
Replies
14
Views
1K
Replies
1
Views
3K
Back
Top