What was perhaps the best experience that I had while on vacation in Montreal, Canada was tobogganing. Tobogganing just means going down a hill of snow on a simple sled (called a toboggan). The picture below is one of my cousins tobogganing by a hill at Beaver Lake. And since it is the Winter Olympics, I thought this blog would be appropriate : )
While sledding towards the bottom of the hill, there are three forces acting on my cousin. The first is weight and the second is the normal force which is perpendicular to the sloped surface of the hill. The third is the force of friction from the contact between the sled and the snow which goes in the opposite direction (up) than my cousin's motion down the hill.
As we've done more than a thousand times before, a FBD would ilustrate that the vertical component of the force of gravity mg cancels the normal force N. Thus, the force that causes the motion downwards is the pull of the horizontal component of force mg, which is mgsin(theta). Although weight mg is constant as he goes down the hill, friction, specifically kinetic friction, and wind resistance slows my cousin down. Because the contact between the toboggan and the snow / ice creates a frictional force that is directed opposite (back up the hill)his direction, the force decreases his rate of acceleration. Therefore, because friction is an important factor in determining one's speed downhill, one should choose a material that has a low coefficient of kinetic friction in order to decrease the negative acceleration done by frictional force F. In my cousin's case, because he chose a plastic sled which has a greater coefficient of kinetic friction compared to a wooden or steel sled, his overall speed all the way down the hill is less.
Furthermore, while others, who are not as "physics-proficient" as we are under the all-knowing guidance of Doc, believe that the fatter you are, the faster you'll go down the hill. HOWEVER, since acceleration due to gravity is constant regardless of the mass, the acceleration of an object down an incline does not depend on mass. If we ignore wind / air resistance, as stated above, the weight (force) of a body of mass m down the hill is given by the equation: F=mgsin(theta) while the frictional force F is given by the equation: F=umgcos(theta). Thus, the net force is given by the equation: F=mg(sin[theta] -ucos[theta]). As a result, acceleration is given by the equation: a=g(sin[theta]-ucos[theta]) since mass from the net F equation and mass in F=ma cancels each other out. The resulting accelaration equation then proves that acceleration down a sloped surface (like a snow-covered hill) is independent of mass.
As we've done more than a thousand times before, a FBD would ilustrate that the vertical component of the force of gravity mg cancels the normal force N. Thus, the force that causes the motion downwards is the pull of the horizontal component of force mg, which is mgsin(theta). Although weight mg is constant as he goes down the hill, friction, specifically kinetic friction, and wind resistance slows my cousin down. Because the contact between the toboggan and the snow / ice creates a frictional force that is directed opposite (back up the hill)his direction, the force decreases his rate of acceleration. Therefore, because friction is an important factor in determining one's speed downhill, one should choose a material that has a low coefficient of kinetic friction in order to decrease the negative acceleration done by frictional force F. In my cousin's case, because he chose a plastic sled which has a greater coefficient of kinetic friction compared to a wooden or steel sled, his overall speed all the way down the hill is less.
Furthermore, while others, who are not as "physics-proficient" as we are under the all-knowing guidance of Doc, believe that the fatter you are, the faster you'll go down the hill. HOWEVER, since acceleration due to gravity is constant regardless of the mass, the acceleration of an object down an incline does not depend on mass. If we ignore wind / air resistance, as stated above, the weight (force) of a body of mass m down the hill is given by the equation: F=mgsin(theta) while the frictional force F is given by the equation: F=umgcos(theta). Thus, the net force is given by the equation: F=mg(sin[theta] -ucos[theta]). As a result, acceleration is given by the equation: a=g(sin[theta]-ucos[theta]) since mass from the net F equation and mass in F=ma cancels each other out. The resulting accelaration equation then proves that acceleration down a sloped surface (like a snow-covered hill) is independent of mass.
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