Newton's Cradle: Does it Really Demonstrate P = mv and E = 1/2mv^2?

[HoloBarre]

I have asserted that Newton's Cradle does not demonstrate specifically that P = mv or that E = 1/2mv^2.

Rather, that it demonstrates only that two *different* laws of motion/conservation are simultaneously at work.

An alternative form of this assertion is that by observing Newton's cradle, you cannot *specifically* derive the above two equations, but rather only an infinite number of pairs of *consistent* equations.

Opinions?

Thanks,

HB

 

[bp_psy]

I have asserted that Newton's Cradle does not demonstrate specifically that P = mv or that E = 1/2mv^2.

Those are mathematical formulations of the definitions of momentum and KE, therefore you don't have to "demonstrate" them.In the case of KE the formula can be derived from other definitions but in the end is still a definition.in the case of momentum p=mv and that is that.

Rather, that it demonstrates only that two *different* laws of motion/conservation are simultaneously at work.
HB

I always considered it a cool toy that shows the conservation laws.

An alternative form of this assertion is that by observing Newton's cradle, you cannot *specifically* derive the above two equations, but rather only an infinite number of pairs of *consistent* equations.

What pairs of equations are you referring to?

 

[astrokreng]

I can understand your assertion that Newton's Cradle does not specifically demonstrate P = mv or E = 1/2mv^2. While it may seem like the motion of the balls in the cradle follows these equations, it is important to note that there are other factors at play such as friction and air resistance. Therefore, it is not a precise demonstration of these equations.

However, I would argue that Newton's Cradle does provide a visual representation of the concepts of momentum and kinetic energy. The transfer of energy and momentum from one ball to the next can be seen and understood through this simple model. It may not be a direct demonstration of the equations, but it does help to illustrate the principles behind them.

Furthermore, I believe that your alternative form of the assertion is also valid. By observing Newton's Cradle, we can derive an infinite number of pairs of consistent equations that describe the motion of the balls. This is because the cradle follows the laws of conservation of momentum and energy, which have multiple mathematical representations.

In conclusion, while Newton's Cradle may not specifically demonstrate P = mv or E = 1/2mv^2, it does provide a visual representation of the concepts and helps us to better understand these fundamental laws of motion and conservation. It is a useful tool for learning and teaching these principles, but it should not be relied upon as a precise demonstration of the equations.