An object with a mass of m = 12.0 g is falling through a resistive fluid in which g is constant. The drag force due to the fluid is F = bv, where F is the force in newtons, b is a constant, and v is the speed in meters per second. If F = 3.2 * 10^-2 N when v = 16.0 m/s, the terminal speed of the object falling through the fluid is A) 0.12 m/s. B) 59 m/s. C) 0.19 km/s. D) 16.0 m/s. E) None of these is correct.

Question

Quizplus · Accepted Answer

Terminal speed is the constant speed at which the object falls when the drag force equals the weight of the object (i.e. net force is zero).

At terminal speed, we have:
F = bv = mg

where m is the mass of the object and g is the acceleration due to gravity. Solving for v, we get:

v = mg/b

We are given F = 3.2 * 10^-2 N and v = 16.0 m/s when the object is falling. Therefore:

3.2 * 10^-2 N = b * 16.0 m/s

b = (3.2 * 10^-2 N) / (16.0 m/s) = 2 * 10^-3 N s/m

Substituting b and m into the equation for terminal speed, we get:

v = mg/b = (0.012 kg)(9.81 m/s^2)/(2 * 10^-3 N s/m) = 58.86 m/s

Therefore, the best choice is B: 59 m/s.

An Object with a Mass of M = 12