Motion Diagram Ball Up Bounce Again
PHYSICS OF BOUNCE
Rod Cross, Physics Dept, Sydney Academy Updated June 2014
The photo above shows the footprint of a loftier speed rubber ball incident from the left on chalk on a blackboard. The ball slides at the start of the bounce and sweeps away the chalk. It and so grips the board and rolls over the chalk. The two dashed lines on the lath are 100 mm apart.
Click the photo to run into a fascinating series of bounces of a spinning superball, filmed in tedious move. It is mesmerizing. The brawl retraces its incident path when it bounces on the right mitt side of the table. The ball grips the table during each bounce and reverses both its direction of motion and the spin direction. There is a lot of interesting physics in both of these events.
A fundamental physics trouble in ball sports is to mensurate or calculate the way the ball bounces. The following diagram illustrates the trouble. If a ball is incident at a certain speed and angle on a surface, then how fast does it bounce, at what bending, and with how much spin?
The problem is more complicated than ane might expect. There is a vertical force N, called the normal reaction force, which acts to change the vertical speed of the brawl, and at that place is a horizontal friction force, F, that acts to alter the horizontal speed of the ball. In add-on, F exerts a torque on the ball that changes its rotation speed. If Due north acts along a line that does not laissez passer through the center of the ball, so N also exerts a torque on the ball.
If the ball slides throughout the bounce then F/N = coefficient of sliding friction. But that happens only if the ball is incident at a glancing angle to the surface, typically about 20 degrees or less. At larger angles of incidence, the bottom of the ball will come up to a stop earlier the ball bounces, and grip the surface, in which instance static friction acts on the brawl. F is and then determined by rubberband distortion of the ball in a direction parallel to the surface, and acts as a shear force. F can even reverse direction during the bounce.
The simplest way to determine how the ball bounces is to film the bounce and and so measure what happens from the film. The ratio of the vertical speed after the bounciness to that before the bounce is called the COR (Coefficient of Restitution). We tin can also define a horizontal COR in an analogous style, in terms of the horizontal speed of the contact bespeak at the lesser of the ball. The horizontal speed at the bottom of the brawl depends on how fast the ball is spinning, besides every bit on the horizontal speed of the centre of mass of the ball. A superball has a horizontal COR virtually 0.5 or 0.six, whereas most other balls accept a lower horizontal COR, typically about 0.1 or 0.2. The vertical and horizontal COR also depend on the elastic backdrop of the surface. For instance, if the surface is rubber rather than concrete then the horizontal COR will exist larger and the ball volition spin faster afterwards it bounces.
GRIP DURING BOUNCE
The post-obit images were taken from video movie of a hollow rubber ball incident obliquely on a smoothen block of granite. The brawl was filmed at 1200 frames/sec. The vertical dashed lines pass through a stock-still point on the granite surface. Equator lines were drawn on the brawl to measure its rotation during the bounciness. The images testify two interesting results. The first is that the bottom of the ball gripped the surface during most of the bounce. The bottom of i equator line remained firmly attached to the dashed lines, rather than sliding forward. The ball moved forward like a bulldozer or an regular army tank on catterpillar track. The second is that the ball get-go leans forrard in frames 1 and 2, due to its high initial speed, then it leans backwards in frame 4. The ball therefore vibrates sideways, and causes the friction strength on the bottom of the brawl to reverse direction. As a event, the ball spin at beginning increases during the bounce and so it decreases. The angle shown in each frame is the modify in rotation angle from one frame to the side by side.
BOUNCE Moving-picture show
Baseball bounce (At 1000 f/s) Tennis ball bounce (At k f/s)
Superball 1000 f/s (annotation spin reversal)
Lawn tennis BALL at 3000 f/s incident at 30 m/s on dirt and on grass (copyright by ITF). Can be viewed with QuickTime or RealPlayer and is in H.264 compressed format. Note how dirt sticks to the ball and is and so spun off. The grass here was longer than normally seen at Wimbledon. Grass is a faster surface than clay, even when the grass is long. You lot can work out the bounce speed, spin and bending yourself from this motion-picture show.
HOOP Bounce1, Bounce2, Bounce3 at 600 fps (taken with a Casio EX-F1 camera).
The hoop slides then grips before bouncing, in the same but in a much more obvious manner than a ball. It is too obvious, peculiarly in bounce2, that the normal reaction strength does not act through the centre of mass and therefore exerts a stiff torque on the hoop, reducing the spin rate. The aforementioned effect occurs with spherical balls. If one part of a ball stops rotating while the rest of the ball continues to rotate, what and then happens to the ball? The hoop flick here helps to answer that question. The hoop behaves as a system of inter-connected particles rather than as a rigid object. The angular momentum of the system is well-defined, fifty-fifty though the angular velocity and moment of inertia are non.
Lawn tennis STRINGS at 600 fps with 25 k/s tennis ball incident on a paw-held racquet. 4 different strings showing string movement: String1 String2 String3 String4. You lot demand to advance i frame at a time to come across the motion. Notation that strings return to their original position very quickly, at least when new, thereby enhancing the spin of the outgoing ball (as explained in the pretty motion-picture show below). That�s why Hewitt has stopped niggling with his strings so much between points.
BOUNCE OFF A FLEXIBLE SURFACE
This is a pretty motion picture of a golf game brawl and an 8mm thick slice of a large superball sitting on a slab of polished granite. The brawl spins faster when information technology bounces off the superball slice since the tangential coefficient of restitution is much larger. A golf ball that spins faster will travel further. Click on photo to see a simplified caption of why the ball spins faster. The aforementioned outcome occurs with lawn tennis strings.
SUPERBOUNCES (Oct 2007, Dec 2009)
A popular physics sit-in is to drib two assurance together, say a tennis ball on tiptop of a basketball. The tennis ball so bounces with almost 16 times more energy, by bouncing off the basketball, than it does past billowy directly off the flooring. A mutual, simplified explanation is that the basketball bounces commencement and then makes a second standoff with the incoming tennis ball. In fact, both balls bounce together (unless the tennis ball is deliberately or accidentally dropped shortly after the basketball game). Come across for yourself, at 300 frames/sec, here.
A detailed explanation of the process involved is given in American Journal of Physics, 75, 1009-1016 (2007). If the bigger brawl is on meridian, then the small ball gets trapped between the large brawl and the floor and can bounce many times before the two balls split. A picture show is shown here, but the multiple bounces tin�t be seen in the movie since they happen too quickly. They can be seen much more easily by bouncing the balls off a piezo disk or force plate, as described in the AJP newspaper.
Bound Bounce (Jan 2008, Nov 2009)
When a ball bounces, the force on the brawl increases to a maximum when the ball pinch is a maximum, and so drops back to zero at the finish of the bounce menses. The force varies in a sinusoidal manner. When a spring bounces on its finish, the force remains abiding in time while a compression moving ridge travels up to the top end, reflects, and travels back to the bottom cease. Then the force drops to nada and the spring bounces. A 300 frames/sec motion picture showing the compression wave can be seen hither (taken in sunlight with a Casio EX-F1 camera using i/4000s exposure). The bounce is also shown in the diagram below. The motion picture is played dorsum at xxx fps (in deadening motion). Notation also that the bottom of the spring starts falling well Subsequently the top is released!
An interesting feature is that the spring bounces after the wave makes 2 trips (1 up and one down) forth the spring. When a steel ball bounces, a compression wave travels up and downwards the brawl well-nigh xv times before the ball bounces. The strength on the ball is non abiding like it is for a spring since it takes a long fourth dimension for the lesser of the ball to compress and then expand.
When ii springs or two rods collide, and if the lengths are different, so kinetic energy is not conserved since the long rod or the long leap is even so compressed at the end of the collision. When two steel balls collide, kinetic energy is conserved even if the assurance are of different diameter. The reason is that wave motion during a collision between two balls plays a neglible role. Almost all the rubberband energy in the ii balls is stored in the small contact volume and very footling energy is coupled to propagating waves since the standoff is spread out over a long time. The collision takes a long time because the contact area is quite small and relatively soft compared with the residuum of the ball. The difference between ball and spring collisions is described in more detail hither.
SLINKY DROP (January 2008, Nov 2009)
When a slinky spring is suspended at its meridian stop and then released, will the whole spring autumn vertically every bit soon every bit the peak terminate is released? Or volition the bottom end fall first? Or will the top terminate fall first? Think information technology through then bank check your answer here (filmed at 300 frames/sec). Information technology�due south quite surprising. Encounter Am. J. Phys. p 583 - 587, July 2007 for an explanation.
A similar thing happens when a player strikes a ball with a bat or club or racquet. The impact sends a transverse wave along the implement, merely the ball is well on its way by the fourth dimension the bending wave arrives at the histrion�s hands. So, anything fancy the player does with the hands during or after striking the brawl is purely for evidence. The merely role of the hands after the bear on is to bring the implement to a stop.
ODD-BALL BOUNCES
Nigh balls used in sport are spherical. Some are elongated, like oval shaped footballs. They are subject to the same footing reaction and friction forces as any other ball, but the normal reaction force rarely acts through the heart of mass of the ball. This results in a novel bounce effect whereby elongated assurance tend to bounce in the direction they are pointing when they striking the ground. To report this upshot, I made a fat pencil from a plastic tube with an eraser stuck in one end. The bounce of such an object can be quite agreeable, as shown in the attached motion-picture show. The bounciness of such an object shows clearly that static friction is oftentimes more of import than sliding friction during the bounciness. Sliding friction can bring an object to residue in the sliding direction but it can�t contrary the management of movement and it tin�t accelerate an object in the sliding direction. Only static friction tin practise that.
The plus sign on the pencil marks its centre of mass and the vertical white line in the middle of the film is a plumbob. The movie is non very entertaining when viewed in real fourth dimension. You demand to advance it i frame at a time to slow it down.
Falling pencils (or trees or chimneys) can also deport in unexpected ways, as shown in this picture show and as described in this paper.
Football game BOUNCE
Footballs tend to bounce in the management they are pointing when they land, as shown in MovieA. This is not always the case, since the bounce direction also depends on the spin, the direction of the spin and the initial forward speed. MovieB shows the unexpected nature of some football bounces. These ii movies were filmed at 25 frames/s but each frame was divide in one-half. The top one-half was recorded ten ms before the bottom half, the fourth dimension interval between each frame being xl ms in both halves of the picture show. Other bounces are shown on the Motion picture Clips page.
A scientific paper on this subject, including the results of 200 different bounces at various angles and spins, can be downloaded as a 700 kb pdf file.
STRESS IN A Billowy BALL
Maximum stress in a brawl occurs in the small region where the brawl contacts the surface. A rough indication of the stress pattern is shown in the following photos of a 1 mm thick sail of polycarbonate compressed border-on (top to bottom) and viewed through two sheets of crossed polaroid. The polycarbonate canvass was cut with scissors to have a flat surface at the top and a curved surface at the bottom.
The stress is evidently concentrated in the contact region but extends around the edge of the sheet as the compression forcefulness increases due to bending of the polycarbonate sheet. The photos were taken in room light with a sheet of white cardboard at the rear to reflect light through the organization. The polycarbonate sail is betwixt two large sheets of polaroid.
Bounciness WITH TWO SPRINGS
It is non like shooting fish in a barrel to meet by middle what happens to a ball when it bounces.
Here are three bounces using ii springs nether a brass bar to catch the action:
Source: http://www.physics.usyd.edu.au/~cross/BOUNCE.htm