Modeling the fall of an object falling with air resistance

Modeling the fall of an object falling with air resistance

Today, we went to find the equation about the speed and the force of resistance.
There is an expectation that air resistance force on a particular object depends on the object's speed:

And we need to determine the k and n so that we can complete the equation. Therefore, first step is taking the natural logarithm of each side we get:

And then, we need to collect the data about the F and v, so we did this in the Design Technology building and to use video capture.

and then, we can:

1. m=5*1.035 g,v=2.525 m/s
2. m=4*1.035 g,v=2.129 m/s
3. m=3*1.035 g,v=1.641 m/s
4. m=2*1.035 g,v=1.272 m/s
5. m=1*1.035 g,v=0.922 m/s

Because we already know the net force :

=>

When the velocity did not changed and be constant, the a =0.

=>

=>

=>

And then,we use the computer to get terminal velocities for each one by fitting the linear portion of the position vs time graph.

Therefore, we get n= 1.39, k=0.0142.

After that, we use Excel to model the fall of an object with air resistance.

we can find the a is close to 0, we can see the velocity at that moment. In additional, we can compare the our calculated graphs with our measured graph. And they are almost same.