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If one cone with a diameter of 10 cm and one of 20cm both fall from 2 meters, why will the 20cm one fall slower (focusing on air resistance and surface area)?
Question Date: 2013-10-06
Answer 1:

As you probably know, in the absence of air resistance, all objects near the earth fall at the same acceleration of 9.8 m/s2, no matter their shape or size, and thus hit the ground at the same time.

In the presence of air resistance, there is now an upward force acting to slow down the objects as they fall. In your question, you asked about cones with 10 cm vs. 20 centimeter diameter. We need to specify an additional assumption.

I will assume that the mass of the two cones is the same. So, I´m imagining that you made two different cones out of the same ball of clay, the first one is taller and skinnier (10 cm diameter) and the second one is shorter and fatter (20 cm diameter). Now the main difference is the cross sectional area of the falling object.

It´s the cross-sectional area (not the total surface area) of the object which matters most in a simple model of air resistance. The 20 cm diameter cone will have a larger cross sectional area, and will therefore fall slower.

You gave a falling distance of 2 meters. The difference over this short of a fall may be very difficult to measure, and the objects probably won´t reach terminal velocity, but the answer and the reasoning are the same no matter the length of the fall.

Answer 2:

A wonderful answer for this question can be read on cones

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