Forces and Equilibrium

Fluid Resistance or Drag Force Fluid resistance or air resistance is a force in the opposite direction of the object’s motion through that fluid At low speeds this force is proportional to the speed of the fluid. The units for k are Ns/m

Air Resistance In air the fluid resistance is proportional to the velocity squared The units for C are Ns 2 /m 2

Net Force and Fluid Resistance Terminal Velocity

Net Force and Air Resistance

High Speed Drag D = drag force C = drag coefficient (0.4 to 1.0) ρ = density of fluid (air) A = Effective cross-sectional area of the body

Problem 1 For a human body falling through the air in a spread-eagle position, the numerical value of C is about 0.25 kg/m. For an 80 kg sky-diver what is the terminal velocity?

Answer 56 m/s or 125 km/hr

Problem 2 A pitcher hurls a kg baseball past a batter at 40.2 m/s (90mph). Find the resistive force acting on the ball at this time.

Answer From Table

Three Types of Equilibrium Stable Equilibrium—Center of Gravity is directly below the support Example: punching dummies Unstable Equilibrium—Center of Gravity is above the support Example: pole vaulter Neutral Equilibrium—Center of Gravity coincides with the point of support, the body remains in whatever position it is placed Example: tire on an axis

Problem 1 A man who weighs 800 N climbs to the top of a 6.0 m ladder that is leaning against a smooth wall at an angle of 60° with the horizontal. The non-uniform ladder weighs 400 N and its center of gravity is 2.0 m from the bottom end of the ladder. What must be the coefficient of friction at the ground if the ladder is not to slip?