Resistive Drag Forces AP Physics Mrs Coyle Falling

Resistive (Drag) Forces AP Physics Mrs. Coyle

Falling with Air Resistance- Terminal Velocity http: //www. physicsclassroom. com/mmedia/newtlaws/efff. cfm

Resistive (Drag) Forces • When an object moves through a medium (liquid or gas), the medium exerts a resistive force, R, on the object, opposing its direction of motion. • The magnitude of the drag force depends on: – the medium – the size and shape of the object – the speed of the object • When equilibrium is reached between the drag force and other forces acting on the object, then the object travels with a terminal velocity.

Magnitude of the Resistive Force, R R can depend on v in a variety of ways. Here are two: a)Slow motions or small objects b)Large objects Note: R=bv R = bv + cv 2 b and c are constants, that depend on the medium and the size and shape of the object.

Example 1: Slow speed, small object • Find the expression for acceleration in terms of v, b, g, m. • Answer: a= dv = g- b v dt m

For the same example find the terminal velocity, vt. • a= dv = g- b v dt m • When t=0 then v=0, so a= g • When a=0, terminal velocity is reached: a= 0= dv = g- b v vt= mg dt m b

For the same example the general expression for v is: • v= vt (1 -e-t/t ) • The time constant t = m/b, is the time by which the sphere reaches 63. 2% of its terminal speed.

Air Drag at High Speeds R = ½ Dr 2 Av – D : drag coefficient (for a sphere D=0. 5) – r : density of air – A : cross-sectional area of the object measured in a plane perpendicular to v (for a sphere A= pr 2 ) – v : speed of the object

Example 2: Find the expression for acceleration for a falling object with air resistance. • Ans: a= g-(D r. A) v 2 2 m

For the same example find the terminal speed. • Ans:

Some Terminal Speeds