Question

This interesting activity examines the effect of weight upon terminal velocity. Gather together some nested coffee filters. Leaving them in their original shape, measure the time it takes for one, two, three, four, and five nested filters to fall to the floor from the same height (roughly 2 m). (Note that, due to the way the filters are nested, drag is constant and only mass varies.) They obtain terminal velocity quite quickly, so find this velocity as a function of mass. Plot the terminal velocity, v versus mass. Also plot  v-squared versus mass. Which of these relationships is more linear? What can you conclude from these graphs?

Answer 1

Lets say the drag frce acting on an object be,

, v is the velocity of the object faling down.

Here we have coffee filters.

Terminal velocity is the velocity achived bu the object when the force acting on the body is zero.

In our experiment, apart from the drag force there will also be a forc eof gravity, , acting downwards,

Hence the equation of motion is given by,

When terminal velocity is reached, a =0, ie,

..................(1)

Now, we are given that as filters are nsted the drag reains the same, so the only thing that varies is the mass.

When we add more mass, the m in equation (1) will change and correspondingly the terminal velocity also changes. Let us rewrite our equation that connects mass to terminal velocity,

or, , or  

We can see that the equation is of the form y=mx, hence it is linear and goes as square root function of mass. The corresponding graphs will be,

For ease of plotting, let us take

From these graphs we can conclude that the terminal velociy increases as the sqare root of the mass.