This force also causes the ball to accelerate to the right during impact. This causes the ball to change its original spin direction from clockwise w i to counterclockwise w F, after impact. Since this force F is acting to the right, it torques the ball counterclockwise. Slip velocity is the relative horizontal speed between the ball’s point of impact and the surface it is impacting. The direction of this friction force is opposite the direction of slip velocity between ball and surface, during impact. This friction force is generated by the gripping action of the ball with the surface. This force F is the cause of the velocity and spin (rotation) reversal. The figure below illustrates this.įor simplicity, assume the ball motion is planar (two-dimensional).Īs shown in the above figure, the horizontal force F is the friction force acting on the ball due to contact with the surface, during impact. For example, certain types of balls (such as SuperBalls) can be given a backspin and (after the bounce) the velocity and rotation of the ball will reverse direction. The physics of a bouncing ball can become particularly interesting for certain cases. The velocity V is still pointing upward, and the acceleration a is still pointing downward since the only force acting on the ball in this stage is gravity. In this stage, the ball has fully rebounded and has lifted off from the surface. As a result, the acceleration a is now pointing downward, and the upward velocity V is now decreasing. This means that the only force acting on the ball is gravity. However, since the ball is no longer deformed it has essentially zero contact force with the surface. The velocity V is still pointing upward since the ball is still in the rebounding stage. In this stage, the ball is barely touching the surface. This means that the acceleration a is still pointing upward. As a result, the ball is less deformed than in the previous stage, but is still deformed enough such that it's pushing against the surface with a force greater than its own weight. In this stage, the ball velocity V is increasing and pointing upward since the ball is now in the rebounding stage. This means that point C is at its lowest point. As a result, the acceleration a is still pointing upward, and the velocity V is zero. In this stage, the ball has reached its maximum deformation. As a result, the acceleration a is pointing upward. This means that the ball has deformed enough such that it's pushing against the surface with a force greater than its own weight. However, the ball has deformed sufficiently such that the acceleration a is now pointing upward. The velocity V is still pointing downward. The velocity V and acceleration a (equal to g) both continue to point downward. It continues to fall vertically downward under the influence of gravity. In this stage, the ball begins to make contact with the surface. (Note that the acceleration due to gravity is g = 9.8 m/s 2, on earth). The magnitude of a is equal to g, in the absence of air resistance. In this stage, the ball falls vertically downward under the influence of gravity ( g). Let's further assume that the ball has uniform density, which means that point C of the ball coincides with its center of mass. Let's define the geometric center of the ball as point C, the velocity of point C as V, and the acceleration of point C as a. To simplify the discussion let's assume that the bounce surface is hard (rigid), and that air resistance is negligible. In this explanation, the bouncing ball physics will be broken down into seven distinct stages, in which the ball motion (before, during, and after impact) is analyzed. To begin this explanation let's first consider what happens to a typical rubber ball that is dropped vertically onto a flat horizontal surface, and which falls under the influence of gravity. But what isn't known to most is what is specifically happening to the ball before, during, and after its brief impact with the surface. Normally we don't think about the physics of bouncing balls too much as it's fairly obvious what is happening – the ball basically rebounds off a surface at a speed proportional to how fast it is thrown. These principles will be discussed.Īlmost everybody, at some point in their lives, has bounced a rubber ball against the wall or floor and observed its motion. Bouncing ball physics is an interesting subject of analysis, demonstrating several interesting dynamics principles related to acceleration, momentum, and energy.
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