0 In downhill speed skiing a skier is retarded by both the...

0 In downhill speed skiing a skier is retarded by both the air drag force on the body and the kinetic frictional force on the skis. (a) Suppose the slope angle is u 40.0°, the snow is dry snow with a coefficient of kinetic friction mk 0.0380, the mass of the skier and equipment is m 85.0 kg, the cross-sectional area of the (tucked) skier is A 1.30 m2, the drag coefficient is C 0.150, and the air density is 1.20 kg/m3 . (a) What is the terminal speed? (b) If a skier can vary C by a slight amount dC by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed?

0 In downhill speed skiing a skier is retarded by both the air
drag force on the body and the kinetic frictional force on the skis.
(a) Suppose the slope angle is u 40.0°, the snow is dry snow with a
coefficient of kinetic friction mk 0.0380, the mass of the skier and
equipment is m 85.0 kg, the cross-sectional area of the (tucked)
skier is A 1.30 m2, the drag coefficient is C 0.150, and the air
density is 1.20 kg/m3
. (a) What is the terminal speed? (b) If a skier
can vary C by a slight amount dC by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed?

Key Concepts

Parameter Sensitivity Analysis

Parameter sensitivity analysis involves studying how small changes in system parameters, such as the drag coefficient, can affect the outcome, like the terminal speed. This type of analysis helps in understanding the responsiveness of a model to variations in one or more parameters, which is crucial in optimizing performance or predicting system behavior under slight modifications.

Kinetic Friction

Kinetic friction is the force that opposes the relative motion of two surfaces in contact when one is moving over the other. It is characterized by a coefficient of kinetic friction which, together with the normal force, determines the magnitude of the friction force acting opposite to the direction of motion.

Force Equilibrium in Dynamics

Force equilibrium in dynamics refers to the condition where all forces acting on an object balance out, resulting in zero net force and thus no acceleration. For an object on an inclined plane, this equilibrium is achieved when the downhill gravitational force is balanced by retarding forces such as friction and drag, leading to a constant terminal speed.

Terminal Velocity

Terminal velocity refers to the constant speed an object reaches when the net forces acting on it balance such that acceleration ceases. In dynamics, achieving terminal velocity means that the driving forces, such as the gravitational component along a slope, exactly counteract the retarding forces like air drag and kinetic friction, making the net force zero.

Air Drag and Drag Coefficient

Air drag is the resistive force exerted by the atmosphere on a moving object and is typically dependent on factors such as the object’s cross?sectional area, the air density, and the drag coefficient. The drag coefficient is a dimensionless parameter that quantifies the drag per unit area and velocity; it plays a crucial role in determining how efficiently an object moves through air.

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