Squash Ball and Temperature Investigation

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Squash Ball and Temperature Investigation

Aim

        This investigation will be looking at what factors affect the bounce of a squash ball (in terms of how high it bounces).

Hypothesis

        Having applied my knowledge of the kinetic theory, I believe that the squash ball will bounce higher as the temperature gets higher up to a certain degree. Then, however, I believe that after a certain temperature, the ball will begin to melt and therefore, the bounce of the ball will decrease.

Prediction

To understand what happens to a ball when it is dropped, we must look at the physics behind it relating to the energy transfers. When you hold a ball above a surface, the ball has potential energy. Potential energy is the energy of position, and it depends on the mass of the ball and its height above the surface (the higher the ball is and the heavier the mass of the ball is, the more potential energy it possesses). The formula for calculating potential energy is PE = mgh where m is the mass in kilograms, g is the gravitational acceleration constant of 9.8m/s2, and h is the height of the ball in metres. As the ball falls through the air, the potential energy changes to kinetic energy. Kinetic energy is the energy of motion. The formula for calculating kinetic energy is KE = ½ mv2, where m is the mass in kilograms and v is the velocity (or speed) in m/sec2. Both potential and kinetic energy have units of Joules (J).

As the ball falls through the air, the Law of Conservation of Energy is in effect and states that energy is neither gained nor lost, only transferred from one form to another. The total energy of the system remains the same; the potential energy changes to kinetic energy, but no energy is lost.

When the ball collides with the floor, the ball becomes deformed (change shape or “flattened”). If the ball is elastic in nature, the ball will quickly return to its original form and spring up from the floor. This is Newton’s Third Law of Motion – for every action there is an equal and opposite reaction. The ball pushes on the floor and the floor pushes back on the ball, causing it to rebound. Solid objects have well-behaved molecules and atoms that line up in an even pattern and give the object a specific shape. A solid has a fixed shape. In dynamics, this is called a "non-deformable" body (the shape does not change). No matter how hard a solid is squeezed or pulled, its molecules do not move closer together or further apart. The object may break, but the molecules don't move. This is an "incompressible" object. Gases, like air, (inside the ball) have even less-organized molecules. Gases take the shape of their containers, and also expand or contract to fill the container. The gas in a squash ball fills the entire inner core of the ball. A gas can be expanded or compressed. As the ball strikes the floor the bottom of the ball is pushed in. The material is pliable and deforms (bends). The compressed (pressed in) ball has less volume than the original uncompressed ball. As the ball comes off the floor the gas and ball material act like a spring and the ball returns to its original shape.  

On a molecular level, most balls are made from am material with long chains polymers. These polymers are tangled together and stretch upon impact. However, they only stretch for an instant before atomic interaction forces them back into their original, tangled shape and the ball shoots upwards.

But why doesn’t the ball bounce back to its original height. Does this invalidate the Law of Conservation of Energy? Where did that energy go? The energy that is not being used to cause motion is changed to heat energy and sound energy. After playing a game of tennis or racquetball, you will notice that the ball is warmer at the end of the game than at the beginning because some of the motion energy has been changed to heat energy. Because bouncy balls have tightly linked polymers, most of the energy is transferred back to motion so little is lost, as sound and heat energy and the ball will bounce well (but it depends on what kind of material the ball is made from).

Now that the general physics behind a bouncing ball can be understood, I can begin to explain my prediction of increasing the temperate of a ball and how this will affect its bounce. A theory, which links into this prediction, is the Kinetic Theory. This is because the Kinetic Theory deals with molecules vibrating and breaking their bonds as they receive more energy. In a squash ball, the air molecules are moving and colliding, pushing against the surfaces they contact, in this case the inside walls of the ball. When the air molecules bounce around inside the ball, they push hard enough on the walls of the round ball to keep its shape, even after it hits the floor. These small pushes, over the entire surface, are defined as pressure and are measured as force per unit area. This is maintained by the constant collisions of air molecules. The pressure of the ball depends on the speed at which the air molecules are colliding and how often they hit the particles of the ball; the more collision that occur in the ball, the greater its air pressure.

When the ball is heated, the heat energy given to the ball will affect the air molecules inside it, giving them more energy to collide and move faster and faster. This would result in more collisions of the air particles with the particles of the ball thus increasing the ball’s overall air pressure.  The "perfect gas law" describes the relation between pressure, density and temperature:

p= ρ RT

where p is the pressure, ρ is the density, R is a gas constant (there is an individual gas constant for each gas) and T is the temperature of the gas. So if the temperature of the gas inside the ball increases and R and ρ stay the same that means the pressure will increase.

        With this increase of air pressure within the ball, the ball will deform less when it comes into contact with the floor than it would when it has a lower air pressure because constant, rapid collisions of the air molecules inside the ball help maintain the shape of the ball better at this higher pressure. Due to the ball deforming (or flattening) less, it loses less sound and heat energy and therefore has more energy to be used in motion resulting in the ball bouncing higher.

        When the ball is cooler or at a lower temperature, the air pressure of the ball is less as the air molecules haven’t got as much energy to collide as fast as a heated ball resulting in poorer maintenance of the balls overall shape and this difference in air pressure of the ball causes the ball to deform more as it hits the grounds making the ball lose more heat and sound energy. This means it has less energy to use during motion, resulting in lower bounces than heated balls.

        I believe that the effect of doubling the temperature of the ball will produce a graph similar to the sketch below:

 

                                        

This is because I believe that as the temperature is doubled, the bounce of the ball will more than double (shown in the graph sketch by the steep curve progressing upwards).  The ball will loose energy in the form of heat and sound energy, discussed above, as it hits the surface of the bench when experimenting resulting in a non-proportional rise with temperature but the height of the bounce will not less than double due to molecular activity being increased as it is provided with more and more heat energy allowing them to move and collide faster and faster. This energy produce by the heat will account for the energy, which is lost as heat and sound.

        The top part of the graph is sketched evening out and is a much less steeper curve because here I believe that after a certain temperature, the molecules of the ball will begin to melt and deform in shape, reducing the overall bounce of the ball.

        Also, the sketch shows the curve not going through the origin of the graph (0,0 point), as I believe that there will still be some molecular activity happening at 00C. If the graph was extended backwards, we may be able to see at which point no molecular activity is taking place. But because the graph would have to be extended backwards, it suggests to me that the temperature at which molecular activity stops would be at a negative value (below freezing).

Apparatus

  • 1 metre rule

  • Clamp to hold the metre rule

  • Stop clock

  • Squash ball

     

  • Kettle

         

  • Thermometer

                         

This apparatus was used in order to accurately measure time and other measurements to gain a reliable set of results. For example, the stop –clock will allow me to time exactly how long the ball should be heated for, the thermometer will allow me to measure the exact temperature of the water in the beaker and the metre rule will allow me to measure the bounce of the ball accurately to the nearest centimetre. Equipment such as the kettle will ensure that water is heated quickly making the experiment quick to do and efficient. This will all help me gain an accurate and reliable set of results.

Safety when Conducting Experiments

Before conducting any experiments, safety procedures and precautions should be taken to minimize hazards and the risks of any accidents taking place.

In this experiment I will be handling hot water from the kettle. Hot water can cause burns and boils to the skin, which are painful. The control measures to reduce the risks are:

  • Don’t handle the kettle yourself; get the teacher’s assistance to help you will filling beakers with hot water.
  • Wait your turn and let your teacher come to your desk to fill your beaker rather than you going to the teacher with empty beakers. This reduces the risk of spillage, as you will not have to return to your desk with a beaker of hot water.
  • Do not leave hot water in beakers near electrical equipment such as sockets or stop watches, as it is highly dangerous if the water is in contact with the electricity causing electric shocks and damaging equipment too.
  • When handling the hot water, make sure you are careful as any spillage of hot water can cause skin burns.
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In the case of an emergency:

  • If burn on skin – Place under a cold tap and leave for approximately 10-15 minutes depending on the severity of the burn. Inform a member of staff immediately and seek medical attention, if necessary.
  • If water is spilt on electrical equipment – Do not touch any of the equipment and immediately inform the teacher of the spillage.
  • If water is spilt on the bench/floor - Don’t immediately wipe up the spillage, as the water will be hot, wait for the water to cool and then mop up the ...

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