THE SPORT
OF VOLLEYBALL
To set a ball, a player wraps her hands around the spherical ball. The
greater the spread of the players hand, the more control she has on
the ball. Once the ball is set, she uses one hand to hit the ball to
a target on the opposite side of the court. Forces are constantly at
play in serves and spiking the ball. The net force on the ball equals
its mass, 0.27 kg, times the acceleration produced by the player. Throughout
the game of volleyball, the mass of the ball remains constant, but the
acceleration and direction of the ball change constantly. According
to the work-energy theorem in physics, work produces a change in kinetic
energy. Work is the dot product of force and displacement and kinetic
energy is 1/2 mass x velocity^2. For the greatest change in kinetic
energy, a large force and "follow-through" are produced by
good players. "Follow-through" creates a larger displacement
for the large force. One of the most exciting moves in volleyball to
watch and to execute is the spike. The tallest players and/or players
with the greatest vertical jump ability execute the spike the best.
To make this maneuver most difficult to return, the projectile (volleyball)
is launched from an angle below the horizontal at high speeds. The higher
the position of launch, the greater the chances of clearing the net
and coming in at a steep angle as well!
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One of the basic laws of physics with race cars is that the wider the car, the faster it corners. Curves on a racetrack offer special challenges to race car drivers because of physics principles. Newton's First Law brings us face-to-face with inertia. Because of inertia, the race car (and driver) would continue on a straight line, non-curving track if some force were not applied. The force must produce a change in direction toward the center of the curve. This type of force that acts perpendicular to the car's velocity is called centripetal force (not centrifugal!). It serves to change direction but not speed. The friction between the tires and the track provide that force. The force is directly related to the square of the speed of the car. If a car goes too fast, the friction force is not great enough to hold the car in the track. The centripetal (center-seeking) force is also inversely related to the radius of the curve. The bigger the radius of turning the less force needed to make the curve. Some tracks are banked (tilted) toward the center of the curving section to help friction hold cars on the track at high speeds. That is also true on exit ramps from major highways.
Baseballs and softballs are examples of sports projectiles. The air
Michael
Jordan seemed to hang in the air forever when he went up for a slam-dunk.
What laws of physics is he breaking? On the ground or in the air, Jordan
is governed by the same laws of physics as everyone else. How high he
goes depends on the force he uses to push on the floor when he jumps.
The harder he pushes, the higher he goes and the longer he stays in
the air. To jump 4 feet vertically -a jump that is very high for a basketball
player-the hang time would be 1.0 seconds. Jordan's dunk is a very exciting
basket that takes place in less than just one second. Jordan makes it
seem longer because when he dunks he holds onto the ball longer than
most players. He actually places it in the basket on the way down from
the top of his leap. He also pulls his legs up as the jump progresses
making the jump look more impressive. Physics affects free-throw techniques
as well in basketball. When a spinning ball bounces, it always bounces
in the direction of the spin on the ball. A backspin on the ball tends
to make it bounce backwards into the basket. Rick Barry, player for
the Houston Rockets, used this backspin technique so successfully that
his free throw percentage was 90%. 
Physicists often view the game of football as one great collision/ projectile/
energy lab. Susan Davis and Sally Stephens put it this way in their
book The Sporting Life; " When two football players collide,
their energy of motion has to go somewhere. That energy goes into deformation,
a nice word for getting smashed." Momentum is the product of mass and
velocity and the energy mentioned above is kinetic energy or ½ mass
x velocity 2. The energy in a collision between two football players
could lift 23 tons of concrete an inch into the air. That energy does
cause severe injuries and damage to the body of the football player.
Physicists find the football an interesting projectile because of its
shape (a "prolate spheroid"). Thrown sideways, the football exhibits
tremendous drag but throw it with the point forward and it slices through
the air. A good quarterback puts a spin of 600 rev/min on the football.
This makes the ball a gyroscope and increases stability. 
Golf
is a game of timing-- as with most sports-- but most golfers can tell
you that small actions can have big impacts especially in this game.
The head of a golf club accelerates about 100 times faster than a very
fast sports car. In about one fifth of a second the club goes from zero
to 100 mph. Quite a takeoff! The impulse (Force x change in Time) of
the impact with the ball propels the ball away from the head of the
club at 135 mph. The club is in contact with the ball only about half
a millisecond (0.0005 s) and any imperfections in a swing can have a
big affect on the way the ball travels in the air. If at impact, the
club head points to the left of the ball's correct path then the ball
will hook; if pointed to the right the ball will slice. Just a one-degree
tilt away from a head-on collision will cause an error of 24 feet off
to the side. Golf is not an easy game! "Keep your eye on the ball!"
applies aptly to golf. At first golf balls were smooth but golfers noticed
that old scuffed balls flew longer. The dimples on a golf ball serve
to reduce the drag on a golf ball somewhat as the stitches on a baseball
also reduce drag. 
Ice Hockey is a grand sport of speed, collisions
and skill. A slapshot can be clocked at
118 miles per hour... and the job of the goalie is to get in the way
of such shots. Collisions on ice are especially tricky because the skaters
are on such a low friction surface. Just as new materials for golf clubs
and tennis rackets have changed the way those games are played, new
aluminum shafts and graphite blades for hockey sticks mean more lightness
and durability. The great Wayne Gretzky of the New York Rangers used
such a stick. Hockey skaters stay close to the ice so their skates can
have taller blades. These skates also have shorter blades to enable
quick turns and stops. Figure skaters leave the ice in a series of leaps
and rotations. Their skates are lower but with longer blades than for
ice hockey. They also have serrated edges at the tips for sudden stops.
Figure skaters practice changing their angular momentum quite a bit.
Angular momentum is the product of Moment of Inertia and Angular Velocity.
Moment of Inertia is the angular counterpart to mass-- it is the measure
of the resistance of an object to changing its angular speed. A figure
skater starts a spin by pulling in his arms to lessen his Moment of
Inertia. By the Conservation of Momentum Principles, the angular speed
must then increase. To come out of the spin, a skater simply extends
her arms to increase angular momentum and decrease angular velocity.
A soccer ball is an Archimedean Solid -a "truncated icosahedron" of
60 vertices and 32 faces. Twelve of the faces are pentagons (5-sided
polygons) and twenty are hexagons (6 sided polygons). There is a carbon
molecule named the "Buckeyball" which has the same shape as a soccer
ball. Force vectors play a great part in directing the kick or a header.
A free kick taken by Brazilian World Cup player, Roberta Carlos reaches
a 70 mph speed with a spin of 600 rev/min. David Beckham uses that spin
to curve a free-kick around a defensive wall and goalkeeper to score
his goals. Physics calculations show that at 25 m from the goal and
a velocity of 25 m/s, Beckham can swing the soccer ball 4.57 m from
the straight path by using spin. Niels Bohr, the famous quantum physicist
and Nobel Prize winner in physics, was an excellent soccer player when
a university student. 
Humans aren't the best swimmers; a sailfish
can swim at 65 mph but humans swim at 5 mph. To move through water,
a swimmer must push on a fluid that is 773 as dense as air and 55 times
as viscous. Swimming uses energy at four times the rate of running.
DRAG FORCE is the biggest factor in cutting back on speed! The main
purpose of kicking is to keep your legs up to reduce DRAG. Eighty percent
of swimming power comes from the arms of the swimmer. All swimmers experience
a drag force from water that sticks to the swimmer to form an adhesive
boundary layer. Swimmers use scientific principles to reduce drag. New
materials for swimsuits funnel water away to reduce drag. 
One of the most striking innovations in field and track was the "Fosbury
Flop". In 1968, Dick Fosbury pioneered a radical new technique
in high jumping in the Olympics. Prior to this time jumpers had cleared
the high jump by running, jumping and while remaining head up throwing
over one leg and then another (straddle style). that meant that their
center of mass must go over the top of the bar. (Your center of mass
is generally located just below your naval.) Fosbury twisted his body
so that he went over head first with his back next to the bar. He developed
the technique by trial and error but physicists were able to explain
why it worked so well. It takes a lot of energy (work done by your legs)
to leap into the air. In the old way of high jumping, the center of
mass of the body had to clear the bar. In Fosbury's new way, he could
arch his body so that his center of mass was outside his body and did
not have to clear the bar. (See diagram). This takes less energy and
that meant this new style caught on very quickly! Incidentally, Fosbury
won the gold medal in high jumping that year.
