PHE 375: Test 2 BOXES

How a Rolling Wheel Makes Use of Static Friction

Many cars are equipped with anti-lock brakes that allow the wheels to continue to rotate while the brakes are progressively applied. This is much better than wheels that suddenly lock and start to skid. A skidding wheel has less traction (grip on the road surface) than a wheel that is non-skidding, and anti-lock brakes stop you from skidding while slowing down your car. Sensors in your car are designed to respond to a sudden reduction in rotation of the wheels. This allows them to continue rolling rather than locking up and causing a skid. With anti-lock brakes, you stop faster and you can continue to steer. This is something you cannot do very well when you are skidding. A skidding tire is slowed by sliding friction between the contact points that are each stationary for one instant after the other. So, a rotating tire is slowed down by static friction, which is more powerful than sliding friction.

Conservation of Linear Momentum

Momentum occurs any time an athlete or an object moves, and it plays a particularly important role in sports and situations in which collisions occur. An easy way to think of momentum is to see it as a weapon that an athlete can use to cause an effect on another object or an opponent. A puck hit with immense velocity by a hockey player can have enough momentum to drive a goalie backward. Why? Because momentum is a function of mass and velocity, and even though a puck is light and has little mass, National Hockey League Players can hit it over 100mph (160km/h). When the puck hits the goalie, the puck and the goalie (plus pads, gloves, mask, skates, and stick) for an instant become a combined mass. The Puck slows and loses some of its momentum. Because the goalie is driven backward, the goalie gains momentum in that direction. A similar example occurs when a tennis ball is served at such velocity that it knocks the opponent's racket backward. This process is due to what is called the conservation of linear momentum. When two (or more) objects interact - for example, when a baseball is struck by a bat or two hockey players slam into each other - the total amount of linear momentum of the two objects of players after the collision will be the same as the total amount that existed beforehand. So if two football layers bring a total of 100 units of linear momentum into a tackle when they collide with each other, then after the tackle, 100 units of linear momentum will still exist. Linear momentum is not gained or, surprisingly lost; we say it is "conserved." The law of conservation of linear momentum is directly related to Newton's third law, which says that every action has an equal and opposite reaction. Using two american football players, Jack and Pete, let's see how the law of conservation of linear momentum works: 1.) If Jack tackles Pete in a game, Jack and Pete exert equal and opposite forces on each other during the tackle for the same period of time. If Jack applies a force against Pete for 1 s during the tackle, then Pete does exactly the same in return to Jack. It may not look this way when you watch a receiver being hit at the instant he receives the ball, but mechanically, this is what occurs. 2.) From this explanation, we can see that Jack and Pete each experience equal and opposite impulses. Equal and opposite impulses means that the product of Jack's force multiplied by the time that he applies his force in the tackle is applied back to him in the opposing direction by Pete [F x t (Jack) = F x t (Pete)]. 3.) Since the impulses that Jack and Pete apply to each other are equal in amount and in opposing directions, the change in linear momentum of both Jack and Pete must also be equal and opposite. As an example, if Pete's linear momentum is increased by a certain amount during tackle, Jack's linear momentum must be decreased by the same amount. 4.) The combined linear momentum of Jack and Pete has not changed in any way as a result of the tackle. Linear momentum has been transferred from one athlete to the other, but there has been no gain or loss in the total linear momentum of the two players. Consequently, we say that the total linear momentum of the two plays has been conserved. Collisions occur throughout sport, and it makes no difference if one object is moving (e.g., a golf club) and the other (a golf ball sitting on a tee) is not moving. The ball gains linear momentum and the club loses some of the linear momentum it had before the impact. Collisions cannot create or dissipate linear momentum. Other examples include hockey players, who can skate at tremendous speed and therefore generate great momentum. They demonstrate their momentum in the bone-rattling body checks that characterize their sport. Likewise, offensive and defensive linemen in the National Football League, with their immense size and great acceleration over 40 yd (36.6 m), generate tremendous momentum. Like the hockey player, the lineman who has the most momentum at impact is likely to dominate in a collision with an opponent. In any of these collisions in sport, all that happens is a transfer of linear momentum from one object to another.

What Does "Momentum and Impulse" Mean in Sport?

Momentum plays a particularly important role in sports and situations where an athlete or an object collide. An easy way to think of momentum is to see it as a weapon that an athlete can use to cause an affect on another object or an opponent. When two players on the football field collide, the player with the greatest momentum will keep moving forward. Players can generate momentum by their own combination of mass and velocity, so it will not always be the heavier player who has the greatest momentum. A lighter player, running faster, can generate momentum and come out on top when compared to a heavier opponent. Impulse is the combination of time and velocity of this force. By cleverly manipulating these components in sport, an athlete can enhance a performance or make it safer (or both). If we look at catching a baseball, the velocity of the ball means that the ball will generate a large momentum. Players going to catch the baseball can manipulate the time over which the force is applied to their hand (impulse) - can increase the time by skillfully allowing their hand to move slowly back at the time of impact. This longer time reduces the impulse force at impact and can reduce injuries to the hand. Fielders in the game of cricket don't wear gloves like those used in baseball. Yet a cricket ball is similar in size to a baseball, but harder. To stop the sting of catching a hard-driven ball, fielders in cricket reach out to catch the ball and, at the instant of contact, quickly draw their hand backward. This increases the time of contact and reduces the impulse force that is felt at the hand.

The Cost of Slowing Down - An Olympic Record?

The blistering-fast world-record time of 9.69 s for the 100 m sprint by Usain Bolt at the 2008 Beijing Olympics was an amazing performance, taking 0.03 s off the original mark he had set in May that year. Watching the race, it was evident that Bolt started slowing down at around the 80 m mark, and the question is raised - what could the world record have been if he had not slowed down? By calculating Bolt's early speed, acceleration, and position prior to effectively switching off and slowing down, it is possible to model and predict the final velocity and subsequently the time to run 100 m. Several people have calculated and predicted the possibilities, such as Norwegian physicist Hans Erikson, who estimates that the Jamaican athlete could have clocked between 9.55 and 9.61 s in China if he hadn't slowed down to celebrate his gold medal effort with about 20 m to go.

Coefficient of Restitution

The coefficient of restitution (COR) is a measure of the ability of an object like a ball to spring back to its original shape after being hit by a club, bat, or racket or after bouncing off a floor or wall. It's essentially a measure of "bounciness" or "resilience." All ball sports have specific rules controling just how much bounce a ball is allowed to have. Rules also take into consideration the composition and manufacture of the club, bat, and racket (and strings). Too much or too little rebound, and the whole character of the sport is changed. The highest COR rating is 1 and the lowest is 0, Children's Super Balls and golf balls have tremendous bounciness and have a COR between 0.8 and 0.9. Tennis Balls have a COR of 0.72. Baseballs are required to have a COR between 0.51 and 0.57, and basketballs must have a COR between 0.76 and 0.80. Squash balls have a COR between 0.34 and 0.57 and are available in wide range of rebound and hang-time ability. This is intended to accommodate the various abilities of different players. In addition, the COR of a ball can vary according to the temperature; as the temperature rises, so does the amount of bounce.

Rebound in Tennis

The game of tennis is in many ways more complex than table tennis because of the number of factors that affect the rebound of the ball. For example, a tennis court can be clay, grass, or a hard surface. All these surfaces have different effects on the way the ball rebounds. Courts can be indoors or outdoors, and environmental conditions such as temperature, humidity, and wind velocities alter play. Tennis rackets vary in size, shape, weight, and flexibility; strings differ in type and tension. Even the tennis ball itself changes the way it reacts. Tennis balls bounce higher after they are warm and after some nap (i.e., fuzz) is worn off. When they have been out of their pressurized cans for a long time, the balls age and lose their bounce irrespective of how much use they've had.

Rules Limit for Jumpers

The rules of high jumping don't reward an athlete who can jump the highest in any style, but rather the athlete who can jump the highest off one food (and then cross a bar). If a two-foot takeoff were allowed, the world record of just over 8 ft (2.4 m) would surely be beaten by a gymnast using a high-speed run-up, a round-off, and several back handsprings to gain speed, followed by a triple back somersault to cross the bar. Today's elite gymnasts reach heights of 9 to 10 ft (2.7 to 3.0 m) on the second of the three somersaults. Forty years ago, using a single back somersault, gymnasts cleared a bar set at 7 ft and 6 in. (2.28 m ). As you can see, different rules are required for high jumping and gymnastics to ensure that the skills of the sport are maintained.

Technology Changes the Tennis Racket

The sweet spot is that part of the tennis racket that returns the ball with the greatest velocity and with the least shock and vibration to the player. Tennis rackets have increased in size 74 sq in. (483 sq cm) for the old wooden rackets to 95 to 100 sq in. (613 to 645 sq cm) for modern composite rackets have a larger sweet spot, which is higher on the racket face. In addition, composite rackets are stiffer so that they transfer more energy to the ball. With a higher sweet spot, the ball is hit more reliably, the player feels less shock and the ball comes off the racket faster.

What Does "Work, Power, Energy, Rebound, and Friction" Mean in Sport?

These terms are important in sport as they can define and quantify the "amount" of movement that has occurred. For example, by knowing how to calculate the work (force x distance) we can compare one athlete's performance to another's, or for the case of one athlete we can determine whether the training the athlete has been doing is effective, demonstrated with an increase in work. Similarly, the important variable of power (force x time) can be quantified, and the more powerful we can help an athlete become the more effective that athlete can be in a range of sports. Understanding the energy that is stored, generated , lost, and translated allows us to "mechanically" skillfully intervene with the athlete's technique and ultimately enhance performance. Finally, knowledge about frictional forces can be utilized both to enhance a performance (e.g., increasing the friction between the ground and the shoes of a lineman will increase his ability to block an opposing player) and to make the sport safer (e.g., reducing the friction between the tennis court and the player will allow the player to slide instead of abruptly stopping when running across the court). Most importantly, measuring these mechanical components will allow provision of objective feedback to the athlete and coach on what they should do in the current sporting activity.

Absorbing the Impact

Air bags in cars act like a pole-vaulter's landing pad: both are designed to absorb impact. A pole-vaulter's landing pads are permanently filled with absorbent material that cushions the athlete's landing. Air bags in cars have to fill at high speed to absorb the impact of a driver or passenger who is thrown forward in a collision. Using the same principle as the air bags in cars, air bubbles cushion springboard and tower divers in training. Pressurized air is released from the bottom of the diving tank. The air expands as it rises and provides an elevated area of frothy water at the surface. There's less punishment if athletes fail a dive because there's a bed of watery air bubbles to land on. Divers can fail in a dive from the 10 m tower knowing that at over 30 mph (48km/h), most of the sting of hitting the water has been eliminated.