How to Use Terminal Velocity to Determine Mass

Terminal velocity is an important factor in determining when a falling object reaches the maximum speed over the course of a fall. Fortunately for physicists and budding scientists, there is an equation to determine terminal velocity. There are times, however, when the only part missing from the equation is the mass, or weight, of the object falling. Follow along to determine mass from the terminal velocity equation.

Instructions

    • 1

      Begin by setting up the equation for terminal velocity, which is as follows: V = sqrt ( (2 * m) / (Cd * r * A)) , where V is equal to terminal velocity, m is mass of the object, Cd is the drag coefficient, r is the atmospheric density and A is the projected, or reference, area of the object.

    • 2

      Square both sides of the equation to eliminate the square root on either side. This will leave you with the following equation: V^2 = (2*m)/(Cd*r*A). Doing this will make it easier to separate m, or mass, from the full equation.

    • 3

      Multiply both sides of the equation by (Cd*r*A), which will leave the equation as follows: (V^2)(Cd*r*A) = 2m.

    • 4

      Divide both sides of the equation by 2 to finally isolate m, or mass, on its own. This will leave you with the following equation: ((V^2)(Cd*r*A))/(2) = m.

    • 5

      Plug in the variables for your equation, aside from mass, and solve. The result you come up with will be mass, or weight, of the object that is falling.

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