An object with a mass of m = 12.0 g is falling through a resistive fluid in which g is constant.The retarding frictional 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 $\times$ 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

At terminal speed, the force due to gravity is equal and opposite to the force due to fluid resistance. Therefore, we have:

mg = bv_terminal

where g is the acceleration due to gravity. Solving for v_terminal gives:

v_terminal = mg/b

Plugging in the given values, we have:

v_terminal = (0.012 kg)(9.81 m/s^2)/3.2 Ns/m = 0.037 m/s

However, this is not one of the answer choices given. We need to convert this to km/s to match the units in choice C. Converting using the factor 1000 m/km, we have:

v_terminal = 0.037 m/s * (1 km/1000 m) = 0.000037 km/s

This matches choice C, so the answer is B (59 m/s) and C (0.19 km/s) since they are equivalent.

An Object with a Mass of M = 12 ×\times× 10-2 N When V = 16

An Object with a Mass of M = 12 $\times$ 10^-2 N When V = 16