Frictional heat generated by the moving ski is the chief...

Frictional heat generated by the moving ski is the chief factor promoting sliding in skiing. The ski sticks at the start, but once in motion will melt the snow beneath it. Waxing the ski makes it water repellent and reduces friction with the film of water. A magazine reports that a new type of plastic ski is even more water repellent and that, on a gentle $203-\mathrm{m}$ slope in the Alps, a skier reduced his time from 61 to $42 \mathrm{~s}$ with the new skis. Assuming a $3.0^{\circ}$ slope, compute the coefficient of kinetic friction for each case.

Key Concepts

Kinematics

Kinematics is the branch of mechanics that deals with the description of motion without considering its causes. It involves using equations of motion to relate displacement, velocity, acceleration, and time. In problems involving objects moving along an inclined plane, kinematics is used to determine the acceleration and velocity profiles from which frictional effects can be inferred.

Normal Force

The normal force is the component of contact force exerted by a surface that is perpendicular to that surface. On an inclined plane, the normal force is reduced compared to the full gravitational force because it is proportional to the cosine of the slope angle. This modification is important since the frictional force, which depends on the normal force, directly influences the motion of the object.

Motion on an Inclined Plane

Motion on an inclined plane involves analyzing forces acting on an object when it is placed on a slope. The gravitational force is decomposed into two components: one parallel to the plane that drives the motion, and one perpendicular to the plane that determines the normal force. This decomposition is crucial for understanding how friction and acceleration affect the object's motion along the slope.

Coefficient of Kinetic Friction

The coefficient of kinetic friction is a dimensionless value that characterizes the resistance to motion when two surfaces slide against each other. It is defined as the ratio of the kinetic friction force to the normal force acting between the surfaces, providing a means to quantify how much frictional force opposes movement. This concept is central to analyzing problems where energy dissipation due to friction plays a key role.

Energy Conservation

Energy conservation in mechanics refers to the principle that the total energy in an isolated system remains constant, transforming from one form to another. In the context of an object sliding down an incline, gravitational potential energy is converted into kinetic energy, while some energy is dissipated as heat due to friction. This approach allows one to relate the work done against friction to the initial potential energy, offering a method to calculate the friction coefficient.

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