Question

Forces that are dependent on VELOCITY are DRAG FORCES. These forces are due to the reaction of the medium to the motion of the object. There are two sorts of these: LINEAR, or VISCOUS drag, models forces proportional to the velocity of the object and occurs in DIFFUSE media at SLOW speeds, and QUADRATIC, or TURBULENT, drag models forces proportional to the square of the velocity and occur in DENSE media or at HIGH speeds.

1. A sailboat is pushed with a linear drag coefficient 63 g/m by wind blowing at a speed 2.42 m/s, while being slowed by a quadratic drag with the still water of 106 g/s.

What is the cruising speed of the sailboat?

Answer 1

Drag Force F_D is found to be proportional to the square of the speed of the object.

Mathematically F_D?V²

F_D=1/2 * C?AV²

where C is the drag coefficient, A is the area of the object facing the fluid, and ? is the density of the fluid.

At low Reynolds numbers you get laminar flow and CD?1/v, while at higher Reynolds numbers there's turbulence, and you get CD roughly constant.

Objects moving at high speeds through air encounter air drag proportional to the square of the velocity. Describing the motion of objects under this quadratic drag usually requires numerical techniques rather than straight analytic formuli since the drag force and the gravitational force are not acting along the same line. The case of the vertical trajectory can be treated analytically since the forces are colinear. It is common practice to express the velocity and time in terms of the terminal velocity v_t and a characteristic time ?.

Velocity with Linear Drag. For an object that is acted upon by its weight, mg, and subject to a drag force proportional to its velocity -bv, the general form for the velocity is given by

V = V_Oe^-t/+ Vt [1 - e-t/]

Given ,

A sailboat is pushed with a linear drag coefficient 63 g/m by wind blowing at a speed 2.42 m/s, while being slowed by a quadratic drag with the still water of 106 g/s.

drag coefficieent Cd = 63 g/m

Velocity of the sailboat V = 2.42 m/s

Air drag coefficient can be expressed in the form of quadratic drag force fd = - CV² = - 63 x 2.42² = -23,244 g/s

balancing with quadratic drag force of 106 g/s.

Net force -23244 - 106 = -23350 g/s

This is the cruising speed of the sailboat.