What Causes a Dropped Ball to Bounce? - MK
What causes a dropped ball to bounce? - MK
When you lift a ball off the floor, you transfer energy to it. This energy is stored in the gravitational force between the ball and the earth and is called gravitational potential energy. When you release the ball, its weight makes it accelerate downward and its gravitational potential energy gradually becomes kinetic energy, the energy of motion. When the ball hits the floor, both the ball's bottom surface and the floor's upper surface begin to distort and the ball's kinetic energy becomes elastic potential energy in these two distorted surfaces. The ball accelerates upward during this process and eventually comes to a complete stop. When it does, most of the energy that was initially gravitational potential energy and later kinetic energy has become elastic potential energy in the surfaces. However, some of the original energy has been converted into thermal energy by internal frictional forces in the ball and floor. The distorted ball and floor then push apart and the ball rebounds into the air. Some or most of the elastic potential energy becomes kinetic energy in the ball, and the rising ball then converts this kinetic energy into gravitational potential energy. But the ball doesn't reach its original height because some of its original gravitational potential energy has been converted into thermal energy during the bounce.
Does the air pressure of a basketball and the hardness of the floor surface have an effect on the height of the bounce? -- BB, West Unity, OH
Yes to both questions. When a basketball collides with the floor, the ball's kinetic energy--its energy of motion--is temporarily stored as elastic potential energy in two objects: the ball and the floor. The fractions of the collision energy stored in the basketball and the floor depend on how far each of them dents--the more one dents, the larger the fraction of the collision energy it receives. How well the basketball rebounds from the floor depends on how much of the collision energy returns to the ball during the rebound. Some of the stored energy in each dented surfaces is converted to thermal energy and is lost from the bouncing process. A hardwood floor is very springy and returns its share of the collision energy efficiently. A properly inflated basketball is also very springy. Thus when a firm basketball bounces on a good hardwood floor, it bounces well. But if the basketball is underinflated, its surface bends too far so that it receives most of the collision energy and internal friction in the ball's skin wastes most of that energy. The ball bounces weakly. And if you try to bounce the ball on a soft carpet, the carpet dents easily, receives most of the collision energy, and wastes most of it as thermal energy. Again, a weak bounce.
Basic Ideas: / Energy can be neither created nor destroyed, but it can be converted from one form to another and it can be transferred from one object to another.During a collision, energy is usually transfered from one object to another.
U = mgh, where U = gravitational potential energy, m = mass, g = gravitational constant, and h = height.
To perform the calculations, we have estimated that shoulder height is about 5 feet or 1.5 meters, above the waist is about 4 feet or 1.2 meters, and below the waist is about 2.5 feet or 0.75 meters.
Step 1: / When the basketball is placed at shoulder height it contains gravitational potential energy, but no kinetic energy. The original gravitational potential energy of the basketball is calculated to be 8.53 Joules. (see below for calculations) When the basketball collides with the floor, some of its energy is lost to the floor and some is lost due to the slight deformity of the ball during the collision. Since the basketball rebounds to above the waist, the rebound gravitational potential energy it now contains is calculated to be 6.82 Joules. This means that approximately 1.71 Joules of energy was transferred to the floor. Doing the same calculations with the racquetball, we see that the original gravitational potential energy is 0.588 Joules, the final gravitational potential energy is 0.470 Joules, and 0.118 Joules of energy was transferred to the floor.
Basketball
Uoriginal = 580 (g) * 9.8 (m/s2) * 1.5 (m) = 8.53 (Joules)
Urebound = 580 (g) * 9.8 (m/s2) * 1.2 (m) = 6.82 (Joules)
Ulost = 8.53 (Joules) - 6.82 (Joules) = 1.71 (Joules)
Energy can be neither created nor destroyed, but it can be converted from one form to another and it can be transferred from one object to another.
During a collision, energy is usually transferred from one object to another.
Energy can be stored in an object by lifting the object to a certain height. This energy is called gravitational potential energy. The gravitational potential energy of an object depends on how heavy the object is and how high it is. The heavier an object is, the more gravitational potential energy it has, and the higher an object is, the more gravitational potential energy it has.
When the basketball falls to the ground or is dribbled (a hand pushes down on the ball) the ball bounces back. This occurs due to the elastic collision that occurs between the basketball and the ground (or more specifically, the air particles in the ball and the ground). A perfect elastic collision is defined as a collision of particles in a closed system in which the total kinetic energy of the particles is conserved. The elasticity of a basketball can be determined by the height the ball rebounds. The basketball cannot achieve a perfect elastic collision with the ground but it can, however, achieve as much as 80% elasticity depending on the air pressure inside the ball.The air pressure of the ball greatly affects the elasticity of the ball and the conservation of energy of the ball. A tightly inflated basketball has a large amount of particles present inside the restricted space the surface of the basketball provides. The picture below represents a tightly inflated basketball. Although air particles are so small in size that they would not be able to be seen and there would be many more particles present inside a basketball than shown here, we will use this picture solely as a visual aid
Air is a gas and because one of the properties of a gas is that its particles are in constant motion, imagine the blue particles above are all independently moving and bouncing off each other and the inside wall of the basketball. Because there are so many particles packed into such a small space, the particles bounce off each other and the inside wall at rapid speeds. When the ball is dribbled and, in the process, hits the ground the opposing force of the ground causes the surface of the ball to dent as shown below.
When the ball dents, the same number of particles that were present before the impact are now pushed into a smaller space and become even more tightly packed and bounce off each other at greater speeds. Because the particles are in such a state, they continue to bounce off each other and the inside wall causing the ball to inflate to its original condition and rebound in the opposite direction.This proves Newton's Third Law, which states that for every action there is an equal and opposite reaction. Which explains why when the ball is pressed in by the floor, the ball exerts an equal and opposite force and bounces back upwards. Now let's take a poorly inflated basketball as shown below.
As before, this basketball also contains a number of air particles all in constant and independent motion continually bouncing off each other. This ball, however, has a substantially smaller amount of air particles present in the same amount of space as the tightly inflated basketball. The particles, therefore, bounce off each other at a slower speed. When the ball dents when being dribbled the particles (as before) are pushed into a much smaller space but, because the ball has a higher capacity for air particles than is present in the ball, the particles bounce off each other and the inside wall at a slower rate causing the ball to inflate to its original condition but rebound in the opposite direction with a lot less force or, depending on the number of air particles present, not inflate or rebound at all.
The condition of the basketball determined by its inflation can also have a great affect on the energy conserved during dribbling. As a basketball drops to the floor, its potential energy is converted into kinetic energy and as the ball rebounds, its kinetic energy is converted into potential energy as shown below.
A tightly inflated ball retains a good portion of its energy when being dribbled. A poorly inflated ball, however, loses a lot of its energy due to friction and a much smaller opposing force which is produced by the air particles inside the ball. The ball, therefore, rebounds with a much smaller amount of energy than it originally had and may not reach anywhere near its original height due to the opposing force of gravity or, if the opposing force of gravity is greater than the rebounding force, the ball will not rebound at all.
With spin, the ball loses a much greater amount of energy due to fiction for, as the surfaces come in contact, the spinning ball rubs up against the surface causing an opposing frictional force. The loss of energy that is caused from this action causes the ball to rebound with a much smaller velocity moving in a different direction and (with the help of gravity) a much lower angle creating a better chance for the shot to be successful.
