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

In summary, the diagram of a pendulum motion experiment shows that drag causes the angle, height, and velocity of the pendulum to be smaller than it would be with no drag. This can be explained by the law of conservation of energy, where the work done by the drag force decreases the kinetic and potential energy of the pendulum. Additionally, the initial velocity of the projectile would not be affected by drag.
  • #1
adenine135
7
0
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)
 
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  • #2
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 =)
 
  • #3
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
 
  • #4
adenine135 said:
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 :smile:

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.
 
  • #5
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?
 
  • #6
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.
 

1. How does drag affect the period of a pendulum?

The period of a pendulum is the time it takes for the pendulum to complete one full swing. The presence of drag, or air resistance, causes the pendulum to lose energy, resulting in a shorter period. This is because the drag force acts in the opposite direction of the pendulum's motion, slowing it down.

2. What factors influence the amount of drag on a pendulum?

The amount of drag on a pendulum is influenced by several factors, including the shape and size of the pendulum, the density and viscosity of the surrounding air, and the speed at which the pendulum is swinging. A larger and more streamlined pendulum will experience less drag compared to a smaller and more irregularly shaped one. Higher air density and viscosity will also increase the amount of drag, as well as a faster swinging speed.

3. How does drag affect the amplitude of a pendulum?

The amplitude of a pendulum is the maximum displacement from its resting position. Drag has a minimal effect on the amplitude of a pendulum, as it only affects the pendulum's motion in the opposite direction of its swing. However, as the pendulum loses energy due to drag, the amplitude will gradually decrease over time.

4. Can drag be completely eliminated in a pendulum?

No, it is impossible to completely eliminate drag in a pendulum as it is always present in the surrounding air. However, the effects of drag can be reduced by making the pendulum more streamlined and minimizing air density and viscosity.

5. How can the effect of drag on a pendulum be calculated?

The effect of drag on a pendulum can be calculated using the drag equation, which takes into account the drag coefficient, the density and velocity of the air, and the surface area of the pendulum. This equation can be used to estimate the amount of drag and its impact on the pendulum's motion.

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