Question

A series of experiments is conducted to analyze the effect of fluid resistance on the motion of various small objects of mass m falling from rest in columns of different fluids. In all cases the acceleration due to gravity is g = 10 m/s2 and the magnitude of the fluid resistance force can be modeled by the equation FR = kv where k is a constant and v is the magnitude of the velocity of the object. Which of the statements below are correct?

The terminal velocity reached by the falling object will be the greatest in the case of the largest mass, regardless of the fluid.

The terminal velocity reached by the falling object will be the greatest in the case of the largest fluid coefficient k, regardless of the mass of the falling object.

The terminal velocity reached by the falling object will be the greatest in the case of the largest ratio k/m.

The terminal velocity reached by the falling object will be the greatest in the case of the smallest ratio k/m.

The terminal velocity will be reached faster when the falling object is heavier, regardless of the fluid.

The terminal velocity will be reached faster when the fluid has the smallest coefficient k, regardless of the object.

The terminal velocity velocity will be reached faster when the ratio m/k is the greatest.

The terminal velocity will be reached faster when the ration m/k is the smallest.

I picked 1,4 and 8 and got partial credit which I think means I am missing another selection(s). Here is the reasoning for my selections (inc = increase, dec = decrease)

Greatest vt?

1. vt = mg/k m inc, vt inc . TRUE

2. vt = mg/k k inc , vt dec FALSE

3. vt = mg/k m:k inc, vt inc. so k:m inc, vt dec. FALSE

4. vt = mg/k m:k inc, vt inc so k:m dec, vt inc. TRUE

Terminal Velocity will be reached faster?

5. v = vt(1 - e^-t/c). c = m/k. m inc then c inc then -t/c dec. FALSE

6. v = vt(1 - e^-t/c). c = m/k. k dec then c inc then -t/c dec. FALSE

7. v = vt(1 - e^-t/c). c = m/k. m:k inc then c inc then -t/c dec. FALSE

8. v = vt(1 - e^-t/c). c = m/k. m:k dec then c dec then -t/c inc TRUE

What am I missing??

Answer 1

1. vt = mg/k m inc, vt inc . TRUE . This has to be FALSE because it can't be greatest for the largest mass without taking the value of K into account. Suppose you have two fluids, one with k and another with k/2 and mass of object in first case is 2m and in second case is m. So if this statement was true the terminal velocity would be greater for 2m mass but it comes out to be equal. So this statement is false.

All the other statements have been marked correctly except the first one.