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Q & A: air resistance in sliding down ramp

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Most recent answer: 09/26/2014
Q:
I have taught physics for 20+ years and I and my students always measure the acceleration of larger masses as larger when they slide down a ramp. I know that air resistance is typically invoked to explain the difference, but I find it hard to believe that air resistance is important for masses that are small (typically less than 1 kg) sliding down a ramp with speeds that are between 1 and 2 m/s. Can you give me an example with numbers that show just how significant air resistance can be with such small, slow moving objects?
- Kimball Clark (age 59)
Gallipolis
A:

That's a great question. How big are the differences? They should become noticeable when the air drag becomes a significant fraction of the net force on the object. Another way to say that is that it's important when the velocity reaches a significant fraction of the terminal velocity, the velocity at which the air drag just cancels the other forces. The terminal velocity will depend on the density and shape of your objects and on the angle of the ramp.  

There's a nice discussion on Wikipedia of the effects of air drag on falling objects: . Using the expressions you can get there, I'm guessing that for your objects falling in the atmosphere terminal velocity would be very roughly 20 m/s. That could vary a lot depending on if they're wood or metal, etc. The key point, however, is that these objects are sliding down a ramp. The net force from gravity and the ramp together is much less than gravity alone, by a factor of sin(θ), where θ is the angle the ramp is tilted. The air drag is not reduced by the tilt, so the terminal velocity will be much lower, maybe about 2 m/s if sin(θ)=0.1. So that's why your objects show different rates of fall. They're getting close to their terminal velocities on the ramp, and those terminal velocities depend on the size of the object.

Mike W.


(published on 09/26/2014)

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