# Acceleration with air resistance

A short while ago, I did an experiment which involed dropping a tennis ball from a height of 2 metres, then measuring it's acceleration. We found the acceleration using computer software, but I want to show how air resistance works against gravity to reduce the ball's acceleration. So in theoy, the formula should be: $$a=F/m$$ with $a$ being the acceleration, $F$ being the net force and $m$ bring the mass of the object. The mass of the tennis ball was 0.006161125kg. The problem I am running into is with the net force. The net force should be equal to the weight of the ball minus the aerodynamic drag: $$F=W-D$$ The weight of the ball is 0.6042kg, and the aerodynamic drag is as follows: $$D=\frac{1}{2}C_dpv^2A$$ With $C_d$ being 0.47 (found off the internet, drag coefficient for a sphere), $p$ being 1.1839kg/m^3, $v$ being 4.756m/s and A being 0.015m^2 (the ball had a radius of 6.86cm).

That gives me a final value of 0.94396922. The problem is when I go to solve for net force: $$F=W-D$$ $$F=0.06042-0.94396922$$ $$F=-0.33976922N$$ This says my net force is -0.33 Newtons, but this can't be correct as the ball continued to accelerate downwards in the experiment. Where did I go wrong?

• Your values appear inconsistent. In addition, kg is mass, not weight, so your units appear to be inconsistent. Furthermore, there are several naked numbers in your work, so it's very difficult to check for dimensional consistency. How do you ensure a constant velocity for a falling ball? – David White Apr 20 '17 at 2:23
• In the software (Logger Pro by Vernier), a table is provided which indicates the object's position and velocity at a particular time. When we weighed the ball, the centigram scale gave us a value of 60.42 grams. I converted it to kilograms, then divided this by 9.80665m/s^2 to get the mass of the ball for the drag calculation. As for the units, this is my first time working with the drag equation, so I converted the raw values to the appropriate units, then inputed them straight into the equation (I got the correct units from the NASA website). – Nathan Chetram Apr 20 '17 at 2:35
• You are in error to divide kg by g to get mass. In your drag equation, the drag coefficient is dimensionless, density is in kg/m^3, velocity is in m/s, and area is in square meters. – David White Apr 20 '17 at 2:40
• Is dividing the weight by the acceleration due to gravity not the correct way to obtain the mass of the object? As for the units in the drag equation, all the variables are using those specific units. I really appreciate your help so far. – Nathan Chetram Apr 20 '17 at 2:47
• I just did the dimensional analysis for the drag equation on paper, and I got the units simplified to kg*(m/s^2), which is the same as using Newtons. – Nathan Chetram Apr 20 '17 at 2:52