Class Notes 4.18.11 Bouncing ball

lab .PE Lab: Finding PE (Mass)

Equation Sheet

Reading Notes:Bouncing Ball Physics

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=345

Retake TEST by Thursday 4.21.11

Hw LATE -50%

Twin Towers worksheet Late -30%

Bouncing ball lab is due

Wednesday by 3pm.

Page 5 space # 3

• Coefficient of Restitution (ELASTICITY) e no label • Coefficient of Restitution COR no label• Height bounce hB meters• Height of the drop hD meters

CONDITIONS FOR USE:

Use to find the COR,

Or to predict how high a resilient object will rebound

Coefficient of Restitution(COR)

• A COR of 1 would be a perfectly elastic collision

• A COR of 0 would be a perfectly inelastic collision.

COR 0 ≤ e ≤ 1• We have dropped various balls and

found the Elastic Coefficient of Restitution

Making restitutionreturn to the way it was

• IF someone

Takes $300 -- repay $300

100% restitution

• Shoplift and do community service

<100%restitution

Approximate coefficient of restitution for different types of balls

type of ball coefficient of restitution

Superball 0.9

Tennis ball 0.75

Baseball 0.55

Foam rubber ball 0.30

Beanbag 0.05

Calculate the Potential energy from the drop height and the bounce height

page 5 space 4

Always positive!

Bouncing Ball • When the bottom gets flatter

• energy is changed to stored energy in the bonds of the ball

• by the bending of the material of the ball

A boulder resting at the top of a hill has

potential energy.

• Gravitational Potential

Energy is the energy stored due to height.• Work can change the

height of the Boulder

• Work can change the

potential energy of the

Boulder

We Graphed all three points, but Average the three trials for PE

Drop HeightBounce #1 Height

Bounce #2 Height Bounce #3 Height

Average Bounce height

20 H20

40 H40

60 H60

80 H80

100 H100

120 H120

140 H140

160 H160

Use the average height for PEDrop Height hD (cm)

AverageBounce

Height hB

(cm)

Drop PED=mghD

Bounce PEcB=mghB

Δ PE(PEB-PED)

20

40

60

80

100

120

140

160

Use the Masser to find the mass in grams

• Be sure to use the same tray of spheres.

• There is only one masser, so please work carefully and quickly.

• Be sure the spheres are in the same tray when you finish.

Mass of bouncing ballThen find PE: in kg and meters

• Find the mass on the balance (take turns) Record the mass in grams on the data table

• Convert the mass to kg ( divide by 1000)

• EX: 35.7 g = .037 kg• Convert the height to m (divide by 100)

• Calculate the PE for the original height (in meters) and the first bounce and record it on the data table you may use 10 m/s/s for the ag in the equation :

PE = mgh

A bouncing basketball captured with a stroboscopic flash at 25 images per second. Ignoring air resistance, the square root of the ratio of the height of one bounce to that of the preceding bounce

gives the coefficient of restitution for the ball/surface impact.

Potential energy changes to kinetic energy due to work done by gravity

PE

Bouncing of ball

• The relative bounciness of different types of balls

• If a soccer ball is dropped on a hard surface, it will bounce back to a height lower than its initial position. Such kind of motion is called the bouncing of the soccer ball, which plays an important role in the motion of the ball. Let us study the mechanism of the bouncing of the ball in details.

• The coefficient of restitution is how you quantify bounciness or give bounciness a number, and you do that by dividing the bounce height by the drop height, then finding the square root of that. When...

Read more: http://wiki.answers.com/Q/What_is_the_Coefficient_of_Restitution_of_bouncing_a_basketball#ixzz1JW73FiKE

• As a result, a ball with smaller coefficient of restitution rebounds to lower height in successive bounces and a shorter time is required for the ball to stop (see below figure). For example, grass reduces the coefficient of restitution of a soccer ball since the bending of blades causes further loss of its kinetic energy. Therefore, it would take a shorter time for the soccer ball to stop if it is kicked on grass instead of hard floor.

The Total Mechanical Energy• As already mentioned, the mechanical energy of an object can

be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME).

• TME = PE + KE

• As discussed earlier, there are two forms of potential energy discussed in our course - gravitational potential energy and elastic potential energy. Given this fact, the above equation can be rewritten:

• TME = PEgrav + PEspring + KE

Mechanical Energy as the Ability to Do Work

changing its temperature.• We can also change the bounciness of a ball by changing its

temperature. Take two baseballs that bounce to about the same height. Put one in the freezer for an hour and leave the other at room temperature. Then compare their bounciness again. You should notice that the room temperature ball bounces a little bit higher. The cold ball would bounce about 80 percent as high as the room temperature ball. Although the difference of bounciness is not dramatic, it's enough to see that temperature can be a factor: it could make the difference between a home run and a pop fly.

• However, the change in bounciness due to the change in temperature is taken for granted for some sport. For example, squash player rely on the pre-game warm up to warm up the ball as well as the players.

Surface bounced on

• Example…grass reduces the coefficient of restitution of a soccer ball since the bending of blades causes further loss of its kinetic energy. Therefore, it would take a shorter time for the soccer ball to stop if it is kicked on grass instead of hard floor.

• Coefficient of restitution of a tennis ball is 0.712. Thanks ...

• 1910 soccer ball [ii] 1950 soccer ball [ii] 2004 Euro Cup ball [ii]

• In the late 1980s, the leather casing ball was replaced by totally synthetic ball in soccer competitions. The covering material of the totally synthetic ball is synthetic leather made from polymer. For high quality ball, the casing is made of the synthetic leather panels stitched together through pre-punched holes by waxed threads. The bladder of a totally synthetic ball is usually latex or butyl bladder. The ball is then inflated by pumping air into its bladder through a tiny hole on the casing. The totally synthetic ball could resist water absorption and reliably maintain its shape.

• The Internal structure of a totally synthetic soccer ball [ii]

• Nowadays, the official soccer rules called the "Laws of the game", which are maintained by the International Football Association Board (IFAB), specify the qualities of the ball used in soccer matches. According to the laws, the soccer ball should satisfy the following descriptions:

• it is spherical in shape, • its casing is made of either leather or other suitable material, • its circumference is not more than 70 cm and not less than 68 cm, • its weight is not more than 450 g and not less than 410 g at the start of the match. • its pressure inside equal to 0.6 - 1.1 atmosphere at sea level.

                                      

          1910 soccer ball [ii]

                                       

            1950 soccer ball [ii]

                                       

            2004 Euro Cup ball [ii]

Figure explaining the extra pressure inside the soccer ball.

The relative bounciness of different types of balls [iii]

• Energy change in the falling ball after release until hitting on the ground.(Note that here "G.P.E." and "K.E." stand for the gravitational potential energy and kinetic energy respectively.)

Work must be done in order to distort an elastic object

• . Therefore, if you pull a spring outward so that it become longer, some energy must have been transferred from yourself to the spring. The energy stored in an distorted object due to its deformation is called the elastic potential energy. So, when talking about the elasticity of the ball, we are indeed talking about the spring-like behavior of the ball. In other words, we are considering the tendency of the ball to return to its original spherical shape when it is being squeezed. Where does the elasticity of the ball come from? The elasticity of a solid ball arises from the elasticity of the constituting material which is due to the interatomic or intermolecular force inside. In contrast, for air-filled ball like soccer ball, its elasticity is resulted from the extra air pressure inside the ball. What happens to a ball after you dropped it above a hard floor? The gravity pulls the ball toward the ground and thus the ball falls leading to the lost of its gravitational potential energy. By the law of conservation of energy, the ball must gain kinetic energy and so it falls towards the ground with an increasing speed. Subsequently, the ball hits the hard floor with a high speed. (Note that the ball always moves with the downward acceleration of g = 9.8 m/s2 as it falls.)

The elasticity of an object means

• the tendency of the object to return to its equilibrium shape, the natural shape of the object with no net force applied on it, when it is being deformed. And the force for the object to restore to its equilibrium shape is called the restoring force, which is always directed in opposite to the deformation of the object. Almost all real rigid body are elastic, i. e. having certain extent of elasticity. A trivial example of an elastic object is the spring. You probably have the experience that a spring would tend to restore to its original size when you stretch it to be longer. Scientist found that, providing the deformation is not too large, the relationship between the distortion and the restoring force is given by the Hooke's law:"The restoring force exerted by an elastic object is proportional to how far it has been distorted from its equilibrium shape." The restoring force Fs on a spring in case of different extension.

• In the law of conservation of energy, it was stated that:"Energy can neither be created or destroyed but can only be changed from one form to another."Therefore, the amount of total energy in an isolated system must be constant. For example, let us consider a piece of charcoal placed in an isolated room. If we burn the charcoal, the chemical energy inside the charcoal is changed into the thermal energy of the room. Then the temperature inside the room would be increased. When the ball hits the ground, the ball exerts force on it. By the Newton's 3rd law of motion, the ground exerts a force on the ball as well. The motion of the ball would be stopped by the (stationary) hard floor resulting in the compression of the ball. So the work done on the ball leads to the increase of the elastic potential energy of the ball. That means some of the kinetic energy of the ball (which is converted from the gravitational potential energy of the ball) is converted into the elastic potential energy when the ball hits the ground. On the other hand, some of the kinetic energy is lost as thermal energy during the impact due to either the internal friction of the ball or the heating of the surface.

• Energy change in the falling ball during the impact

Law of conservation of energy

After losing all the kinetic energy, the ball becomes momentarily at

rest.• The squashed ball would simply act like a compressed spring. The

ball pushes the ground with a restoring force proportional to its displacement from the equilibrium position (Hooke's law). In consequence, the ground pushes back the ball with a force of equal magnitude but opposite in direction. Thus the ball bounces back in upward direction. During the rebound, the stored elastic potential energy is released as the kinetic energy of the ball which is then converted to gravitational potential energy as the ball moves up. Moreover, some of the elastic potential energy is lost again due to friction or heat which results in slight heating of the ball. The ball keeps on going upward until it comes to rest after losing all its kinetic energy again. Due to the lost of some of the initial gravitational potential energy into thermal energy, the ball cannot bounce back to the original height.

What is the Coefficient of Restitution?

(also called: Elastic Coefficient)

What is the slope of each of the graphs?• Use the slope of the graphs to find the

Coefficient of Restitution, just like we did for the Spring Constant.

• The Coefficient of Restitution tells us how “springy” the ball is.

• The slope of the graph represents this constant. The constant will be the same for a given ball.

PE Bouncing Ball Lab

Work and Potential Energy and Problems

Patterns in graphs

Increasing/decreasing/ no change

Linear or curved line of best fit.

Bouncing ball labmeasure height at the first bounce up

and the second bounce

Work to PEor PE to work

• a force acts upon it and changes the height

Measurement of Horsepower• The maximum horsepower

developed by a human being over a few seconds time can be measured by timing a volunteer running up the stairs in the lecture hall.

• If a person of weight W runs up height h in time t, then h.p. = Wh/t X 1/550 ft-lbs/sec.

• A person in good shape can develop one to two horsepower. It will be entertaining to the students if the professor tries it too.

• Should the person be allowed a running start?

http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html

Bouncing Ball

Bouncing a Ball

• What you need:• a tennis ball• a basketball• a room without breakables

• Instructions:Drop the tennis ball from waist height and see how high it bounces.Drop the basketball from the same height and see how high it bounces.Put the tennis ball on top of the basketball and drop them both at arms length from waist height.

•  Results & Explanation:The tennis ball should bounce a lot higher than before. When the balls hit the ground, momentum from the basketball was transferred to the tennis ball making it go much higher than before.