The Effect of Drag on a Pendulum: How Does Drag Affect the Motion of a Pendulum?

[adenine135]

The following link is a diagram of the motion of a pendulum I used in an experiment, where L represents the length of the pendulum arm:

http://farm3.static.flickr.com/2144/2052427314_f42f4cc193.jpg?v=0

Does drag cause the angle θ to be smaller or larger than it would be with no drag?

Does the drag cause the height h to be smaller or larger than it would be with no drag?

Does the drag cause the velocity of the pendulum to be smaller or larger than it would be with no drag?


Thanks! (We haven't covered drag in class yet, so any added insight would be appreciated)

 

[Nabeshin]

Since it appears this is homework, could you first tell us what you know about the problem, what you think might be going on, etc., in an effort to sketch a possible solution? We won't just do it for you =)

 

[adenine135]

Well honestly, we've been taught nothing about the effects of air resistance. Up until now, we were told to assume that air resistance is negligible. Our currently teacher has been out sick for almost 2 weeks and the substitute barely teaches.

The best I can do is guess the answer from common sense, but have no theoretical or quantitative proof to back up my answers:

• the angle would be smaller due to drag
• the height would be smaller due to drag
• the velocity would be smaller due to drag

 

[AlephZero]

The best I can do is guess the answer from common sense, but have no theoretical or quantitative proof to back up my answers:

• the angle would be smaller due to drag
• the height would be smaller due to drag
• the velocity would be smaller due to drag

Your common sense seems to be working OK

One way to think about this is conservation of energy. You can get some useful information from that without knowing enough to solve equations for the "exact" motion of the pendulum.

You don't know enough physics yet to say what the magnitude of the drag force is, but you do know (from common sense) what its direction is.

Work = force x distance.

So as the pendulum moves, the drag force is doing work.

Think about how that work will change the kinetic and potential energy of the pendulum, and how those changes will affect its angle, height, and velocity.

 

[adenine135]

Law of Conservation of Energy:
1/2 m(v_1)^2 + mgh_1 + W_other = 1/2 m(v_2)^2 + mgh_2

So W_other would be the work done by the drag force. But how can I get any supporting evidence for my answers from that?

 

[adenine135]

This is what I've got so far in regards to the ballistic pendulum. I'm not sure if the last one is correct since the question specifically asks if the velocity will be larger or smaller. Also, if anyone can think of a better way to word anything or has any supporting evidence to add, I'd appreciate it.

• the angle would be smaller - drag is a resistive force in the opposite direction
• height would be smaller - the velocity is reduced by drag and, therefore, so is the distance the pendulum travels
• the potential energy would be smaller - since height is smaller due to drag, so is potential energy (PE=mgh)
• velocity of the pendulum and the embedded projectile immediately after impact would be smaller - Drag is parasitic force (subtracting from the force) . Velocity is directly proportional to the force equations. So as drag subtracts from the forward force, the velocity must decrease.
• the initial velocity of the projectile would be smaller - Drag cannot effect initial velocity since it is at time equal to zero essentially. Drag has no time to be induced. Theoretically it would be equal.