Topic: 

NEWTON’S CRADLE MODEL

Group Work

AMNA JALAL

UME HANI ALI

ZEENAT MUJTABA

ZAINAB SHAHID

Abstract:

The Newton's cradle is a device that demonstrates the conservation of momentum and the conservation of energy with swinging spheres. When one sphere at the end is lifted and released, it strikes the stationary spheres, transmitting a pressure or sonic wave through the stationary spheres that creates a force that pushes the last sphere upward. The last sphere swings back and strikes the nearly stationary spheres, repeating the effect in the opposite direction. The device is named after 17th-century English scientist Sir Issac Newton and designed by French scientist Edme Mariotte. It is also known as Newton's pendulum, Newton's balls, Newton's rocker or executive ball clicker.

History:

The principle demonstrated by the device, the law of impacts between bodies, was first demonstrated by the French physicist Abbé Mariotte in the 17th century. His work on the topic was first presented to the French Academy of Sciences in 1671; it was published in 1673 as ("Treatise on percussion or shock of bodies").

Newton acknowledged Mariotte's work, along with Wren, Wallis and Huygens as the pioneers of experiments on the collisions of pendulum balls, in his Principia.

Christiaan Huygens used pendulums to study collisions. His work (On the Motion of Bodies by Collision) published posthumously in 1703, contains a version of Newton's first law and discusses the collision of suspended bodies including two bodies of equal mass with the motion of the moving body being transferred to the one at rest.

There is much confusion over the origins of the modern Newton's cradle. Marius J. Morin has been credited as being the first to name and make this popular executive toy. However, in early 1967, an English actor, Simon Prebble, coined the name "Newton's cradle" (now used generically) for the wooden version manufactured by his company, Scientific Demonstrations Ltd. 

Construction:

The largest cradle device in the world was designed by Myth Busters and consisted of five one-ton concrete and steel rebar-filled buoys suspended from a steel truss. The buoys also had a steel plate inserted in between their two-halves to act as a "contact point" for transferring the energy; this cradle device did not function well because concrete is not elastic so most of the energy was lost to a heat build up in the concrete. 

Operation:

When one of the end balls ("the first") is pulled sideways, the attached string makes it follow an upward arc. When it is let go, it strikes the second ball and comes to nearly a dead stop. The ball on the opposite side acquires most of the velocity of the first ball and swings in an arc almost as high as the release height of the first ball. This shows that the last ball receives most of the energy and momentum of the first ball. The impact produces a sonic wave that propagates through the intermediate balls. Any efficiently elastic material such as steel does this, as long as the kinetic energy is temporarily stored as potential energy in the compression of the material rather than being lost as heat. This is similar to bouncing one coin of a line of touching coins by striking it with another coin, and which happens even if the first struck coin is constrained by pressing on its center such that it cannot move.

There are slight movements in all the balls after the initial strike, but the last ball receives most of the initial energy from the impact of the first ball. When two (or three) balls are dropped, the two (or three) balls on the opposite side swing out. Some say that this behavior demonstrates the conservation of momentum and kinetic energy in elastic collisions. However, if the colliding balls behave as described above with the same mass possessing the same velocity before and after the collisions, then any function of mass and velocity is conserved in such an event. 

Physics Explanation:

Newton's cradle with two balls of equal weight and perfectly efficient elasticity. The left ball is pulled away and let go. Neglecting the energy losses, the left ball strikes the right ball, transferring all the velocity to the right ball. Because they are the same weight, the same velocity indicates all the momentum and energy are also transferred. The kinetic energy, as determined by the velocity, is converted to potential energy as it reaches the same height as the initial ball and the cycle repeats.An idealized Newton's cradle with five balls when there are no energy losses and there is always a small separation between the balls, except for when a pair is colliding Newton's cradle three-ball swing in a five-ball system. The central ball swings without any apparent interruption.

Newton's cradle can be modelled fairly accurately with simple mathematical equations with the assumption that the balls always collide in pairs. If one ball strikes four stationary balls that are already touching, these simple equations can not explain the resulting movements in all five balls, which are not due to friction losses. For example, in a real Newton's cradle the fourth has some movement and the first ball has a slight reverse movement. All the animations in this article show idealized action (simple solution) that only occurs if the balls are not touching initially and only collide in pairs.

Simple solution:

The conservation of momentum (mass × velocity); p=mv and kinetic energy (1/2 × mass × velocity2) KE = ½ mv2 can be used to find the resulting velocities for two colliding perfectly elastic objects. These two equations are used to determine the resulting velocities of the two objects. For the case of two balls constrained to a straight path by the strings in the cradle, the velocities are a single number instead of a 3D vector for 3D space, so the math requires only two equations to solve for two unknowns. When the two objects have the same mass, the solution is simple: the moving object stops relative to the stationary one and the stationary one picks up all the other's initial velocity. This assumes perfectly elastic objects, so there is no need to account for heat and sound energy losses.

Steel does not compress much, but its elasticity is very efficient, so it does not cause much waste heat. The simple effect from two same-mass efficiently elastic colliding objects constrained to a straight path is the basis of the effect seen in the cradle and gives an approximate solution to all its activities.

For a sequence of same-mass elastic objects constrained to a straight path, the effect continues to each successive object. For example, when two balls are dropped to strike three stationary balls in a cradle, there is an unnoticed but crucial small distance between the two dropped balls, and the action is as follows: the first moving ball that strikes the first stationary ball (the second ball striking the third ball) transfers all of its momentum to the third ball and stops. The third ball then transfers the momentum to the fourth ball and stops, and then the fourth to the fifth ball.

Right behind this sequence, the second moving ball is transferring its momentum to the first moving ball that just stopped, and the sequence repeats immediately and imperceptibly behind the first sequence, ejecting the fourth ball right behind the fifth ball with the same small separation that was between the two initial striking balls. If they are simply touching when they strike the third ball, precision requires the more complete solution below.

Effect of different types of balls:

Using different types of material does not change the action as long as the material is efficiently elastic. The size of the spheres does not change the results unless the increased weight exceeds the elastic limit of the material. If the solid balls are too large, energy is being lost as heat, because the elastic limit increases with the radius raised to the power, but the energy which had to be absorbed and released increases as the cube of the radius. Making the contact surfaces flatter can overcome this to an extent by distributing the compression to a larger amount of material but it can introduce an alignment problem. Steel is better than most materials because it allows the simple solution to apply more often in collisions after the first strike, its elastic range for storing energy remains good despite the higher energy caused by its weight, and the higher weight decreases the effect of air resistance.

Uses of Newton's cradle:

Some of the uses of Newton's cradle include:

Demonstrating conservation of energy and momentum: Newton's cradle visualizes an elastic collision by allowing students to see the mass as a number of balls, and the speed as the height the balls travel. This shows that momentum and energy must be conserved.

Teaching physics concepts: Newton's cradle can be used to teach concepts such as elastic and inelastic collisions, gravitational potential energy, and conversion from potential to kinetic energy.

Entertainment: Newton's cradle can be used for entertainment purposes by experimenting with the number of balls pulled back, the amount of energy they start with, and observing the transfer of momentum and energy from one ball to the other.