Week 5 of February 1st
Objectives:
Objectives:
Agenda:
1. Engineering a Smooth Ride ppt.
2. The ski lab done with the assistance from DU
3. Kinematic Equations Worksheet/ Clicker Questions
2. The ski lab done with the assistance from DU
3. Kinematic Equations Worksheet/ Clicker Questions
4. Ski trip paperwork
5. Friction Ppt.
6. Friction Worksheet
Websites:
An object moving through a fluid experiences a drag force in direction opposite to its motion. Terminal velocity is achieved when the drag force Fd is equal in magnitude but opposite in direction to the force propelling the object—the gravity force Fg in this case. Shown is a sphere in Stokes flow, at very low Reynolds number. Small arrows show direction of movement of fluid relative to the sphere.
where
Fd is the force of drag,
is the density of the fluid,
v is the speed of the object relative to the fluid,
A is the reference area,
Cd is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car), and
is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of velocity).
Fd is the force of drag,
is the density of the fluid,v is the speed of the object relative to the fluid,
A is the reference area,
Cd is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car), and
is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of velocity). Friction
Friction is what allows you to stay in control while skiing. It is what slows you down. You apply wax to the base of your skis to try and reduce this in order to go faster. In ski racing it is the person who allows the least amount of friction between themselves the snow and air that wins. In order to stop you use a lot of friction by appling your whole ski edge perpendicular to your direction of travel. With out friction we would not be able to experience the true joy of skiing. The equation for determining the coefficient of friction is µ=Fn/Ff. You can determine how much force the friction if creating by using the equation, Ff=µ(Fn). Ff equals the force created by the friction, and Fn equals the force perpendicular to the direction of travel.
Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.
Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.
Some history of how skis were developed:
One brilliant winter morning in 1929, a young boy named David Lind flung himself down a snowy hill in rural Washington and promptly fell in love. His skis, which he had carved by hand from two hickory planks, weren’t much different from the wooden runners and root bindings used by trappers more than 4,500 years ago, but they made for an exhilarating ride. “They were 7 or 8 feet long and didn’t have much flexibility,” Lind says. They got him down the hill, but just barely in one piece.
Photograph by Grant Delin
Skis have grown ever smaller and shapelier. In the 19th century, Norwegian skiis average 8 feet
in length. Today’s skiis average 5 feet 9 inches.Since that day, Lind has become one of the country’s preeminent authorities on the science of skiing. As a physicist at the University of Colorado in the 1970s and 1980s, he taught a popular course called The Physics of Snow, and in 1996 he co-authored The Physics of Skiing with his son-in-law, Scott Sanders. He was onto something: Science now governs every aspect of the sport, from fabricated snow to skis that are lighter, shorter, more flexible, and far easier to turn. The science behind the skis has triggered nothing short of a revolution in the sport, allowing almost anyone to carve up a mountain slope.
The father of modern skiing was a Norwegian potato farmer named Sondre Norheim. An imaginative freestyler with a habit of jumping off snowcapped rooftops, Norheim created the first heel-strap bindings in the 1860s. He also popularized the zigzag maneuver that became the basis of downhill skiing. A skier who heads straight down a 30-degree slope can reach 150 miles per hour, but traversing back and forth across the slope keeps one’s momentum in check.
More than 100 years passed before the next great leap. In 1989, ski designers in Slovenia took a cue from snowboarders and began to shorten their skis and cut them in the shape of an hourglass. When put on edge, these skis bent at the center, forming an arc in the snow that the board could follow. The radius of the arc was equal to the square of the length between the ski’s two contact points divided by four times the difference between the widest and thinnest points of the ski. In other words, the deeper the side cut, the tighter the turn. Norheim’s skis could carve only swooping curves with radii of 300 feet. Today’s racing skis have four times the side cut and can carve arcs with radii of just 40 feet.
To make a sharp turn on straight skis, skiers have to throw their weight forward and to the side, digging their ski tips into the snow and performing a series of controlled skids. With each skid, the skier’s body faces in a slightly new direction, until it completes the arc and faces forward again. On shorter skis with an hourglass shape, skiers can simply roll their ankles to one side and put their skis on edge. As the wide tip and tail dig into the snow, the ski bends in the middle and begins to turn, carving a path down the slope on its edge. Carving is less physically taxing than skidding. And though the new skis are slower on straightaways—their centers push deeper into the snow, increasing friction—they are faster overall because of their turning ability. They are also just as stable as regular skis.
Ski materials have received an equally extensive makeover. Engineers are continually working to make skis lighter and more flexible to absorb bumps in the snow, while keeping them rigid enough to hold their shape during turns. For that reason, metal skis were introduced in the 1950s. Today’s skis, because of their broader tips and tails, have to endure torsional forces that skis of the past could not have withstood. Most skis are now made of sandwiches of fiberglass,
wood, aluminum alloys, glue, and polymers. The Volant ski company, for instance, uses a heat-treated stainless-steel top sheet, which doesn’t twist much, helping ski edges dig into compact snow during turns. Other ski makers layer their skis with stiff carbon fibers, crisscrossed at 45 degrees to the ski’s long axis. The K2 ski company has even toyed with piezoelectric polymers, which generate an electric charge when twisted. When a skier makes a sharp turn, a semiconductor in the ski sends a countercharge back to the polymer, which dampens vibrations and helps keep the ski’s edge on the snow.
Early skis were like gliding snowshoes, spreading skiers’ weight across the snow to keep them from sinking. The oldest known ski, preserved in a bog in Hoting, Sweden, dates to 2500 B.C. Poems from A.D. 1000 praising Viking ski racers are the earliest records of recreational skiing.
Each new snow season seems to bring remarkable changes. Recently, for example, ski manufacturers have started touting skis with integrated, rather than screw-on, bindings. They are useful on packed snow because they allow skis to bend in a more perfect arc without skidding. Last year, a professional freestyle skier named Shane McConkey designed a pair of skis shaped like surfboards—fatter in the middle than at the ends. In deep powder, McConkey realized, skiers use the middle of their boards to plow through the snow, pushing it aside as if surfing on water.
For his part, David Lind thinks the future of the sport lies in technologies that will let skiers tackle multiple terrain types on the same day. “There are some skis, especially for backcountry use, that have a tension cable built into the base so that you can make the ski stiffer or softer, depending on the snow,” he says. Although Lind now sticks to groomed runs—he is 85, after all—he ignores his doctor’s orders to take it easy: “I still ski as much as I can,” he says. “Fortunately I’m old enough so I can go skiing most places for free.”
Photograph by Grant Delin
Skis have grown ever smaller and shapelier. In the 19th century, Norwegian skiis average 8 feet
in length. Today’s skiis average 5 feet 9 inches.Since that day, Lind has become one of the country’s preeminent authorities on the science of skiing. As a physicist at the University of Colorado in the 1970s and 1980s, he taught a popular course called The Physics of Snow, and in 1996 he co-authored The Physics of Skiing with his son-in-law, Scott Sanders. He was onto something: Science now governs every aspect of the sport, from fabricated snow to skis that are lighter, shorter, more flexible, and far easier to turn. The science behind the skis has triggered nothing short of a revolution in the sport, allowing almost anyone to carve up a mountain slope.The father of modern skiing was a Norwegian potato farmer named Sondre Norheim. An imaginative freestyler with a habit of jumping off snowcapped rooftops, Norheim created the first heel-strap bindings in the 1860s. He also popularized the zigzag maneuver that became the basis of downhill skiing. A skier who heads straight down a 30-degree slope can reach 150 miles per hour, but traversing back and forth across the slope keeps one’s momentum in check.
More than 100 years passed before the next great leap. In 1989, ski designers in Slovenia took a cue from snowboarders and began to shorten their skis and cut them in the shape of an hourglass. When put on edge, these skis bent at the center, forming an arc in the snow that the board could follow. The radius of the arc was equal to the square of the length between the ski’s two contact points divided by four times the difference between the widest and thinnest points of the ski. In other words, the deeper the side cut, the tighter the turn. Norheim’s skis could carve only swooping curves with radii of 300 feet. Today’s racing skis have four times the side cut and can carve arcs with radii of just 40 feet.
To make a sharp turn on straight skis, skiers have to throw their weight forward and to the side, digging their ski tips into the snow and performing a series of controlled skids. With each skid, the skier’s body faces in a slightly new direction, until it completes the arc and faces forward again. On shorter skis with an hourglass shape, skiers can simply roll their ankles to one side and put their skis on edge. As the wide tip and tail dig into the snow, the ski bends in the middle and begins to turn, carving a path down the slope on its edge. Carving is less physically taxing than skidding. And though the new skis are slower on straightaways—their centers push deeper into the snow, increasing friction—they are faster overall because of their turning ability. They are also just as stable as regular skis.
Ski materials have received an equally extensive makeover. Engineers are continually working to make skis lighter and more flexible to absorb bumps in the snow, while keeping them rigid enough to hold their shape during turns. For that reason, metal skis were introduced in the 1950s. Today’s skis, because of their broader tips and tails, have to endure torsional forces that skis of the past could not have withstood. Most skis are now made of sandwiches of fiberglass,
wood, aluminum alloys, glue, and polymers. The Volant ski company, for instance, uses a heat-treated stainless-steel top sheet, which doesn’t twist much, helping ski edges dig into compact snow during turns. Other ski makers layer their skis with stiff carbon fibers, crisscrossed at 45 degrees to the ski’s long axis. The K2 ski company has even toyed with piezoelectric polymers, which generate an electric charge when twisted. When a skier makes a sharp turn, a semiconductor in the ski sends a countercharge back to the polymer, which dampens vibrations and helps keep the ski’s edge on the snow.Early skis were like gliding snowshoes, spreading skiers’ weight across the snow to keep them from sinking. The oldest known ski, preserved in a bog in Hoting, Sweden, dates to 2500 B.C. Poems from A.D. 1000 praising Viking ski racers are the earliest records of recreational skiing.
Each new snow season seems to bring remarkable changes. Recently, for example, ski manufacturers have started touting skis with integrated, rather than screw-on, bindings. They are useful on packed snow because they allow skis to bend in a more perfect arc without skidding. Last year, a professional freestyle skier named Shane McConkey designed a pair of skis shaped like surfboards—fatter in the middle than at the ends. In deep powder, McConkey realized, skiers use the middle of their boards to plow through the snow, pushing it aside as if surfing on water.
For his part, David Lind thinks the future of the sport lies in technologies that will let skiers tackle multiple terrain types on the same day. “There are some skis, especially for backcountry use, that have a tension cable built into the base so that you can make the ski stiffer or softer, depending on the snow,” he says. Although Lind now sticks to groomed runs—he is 85, after all—he ignores his doctor’s orders to take it easy: “I still ski as much as I can,” he says. “Fortunately I’m old enough so I can go skiing most places for free.”
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