What is the relationship between Terminal Velocity/Speed and Mass of an object?
Terminal speed is the speed at which an object falling will reach a constant velocity, due to balance of the force of gravity and the force of drag. At such a point, the following relation applies F_d = m*g In the case of air drag, most likely the flow is turbulent and the regime of drag called Newton drag applies. The alternative is Stokes drag, which exists if the flow is laminar. The following formula for Newton drag works with any flavor of fluid, as long as the flow conditions are turbulent. F_d = 1/2*Cd*rho*A*v^2 where Cd is a unitless drag coefficient depending on shape, rho is the fluid density, A is the effective cross sectional area, and v is the speed. Equate to weight, as per definition of terminal speed: 1/2*Cd*rho*A*v^2 = m*g Solve for v, and subscript with terminal: v_terminal = sqrt(2*m*g/(Cd*rho*A)) Note: this is only true for the situation of vertical motion in initially still fluid, and a situation of only air drag and gravity being the forces acting on the object. S
