Pendulum Question

[HopefulOncoDoc]

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Hey guys I'm having trouble visualizing this but could someone explain why the bottom pendulum system has the greater change in PE? I thought it was the top one since its center of mass was higher..

 

[loveoforganic]

The bigger mass experiences the bigger change in height (larger magnitude of displacement from equilibrium position).

 

[BerkReviewTeach]

Hey guys I'm having trouble visualizing this but could someone explain why the bottom pendulum system has the greater change in PE? I thought it was the top one since its center of mass was higher..

Try redrawing the two pendulums with just one bob at the center of mass. You'll get two pendulums where one has a greater cable length than the other. The system with the greater cable length will experience a greater change in height from highest point to lowest point.

This can be verified if you consider the potential energy equation where PE = mgL (1 - cosine theta). If L increases, then PE increases, so the change in PE must change too.

Does the BR answer explanation show any pictures or is it just words for this one?

 

[Phantastic]

This can be verified if you consider the potential energy equation where PE = mgL (1 - cosine theta). If L increases, then PE increases, so the change in PE must change too.?

The L will be larger both before and after, which could be larger or smaller than the relative difference in PE for a "shorter" arm.

The bigger mass experiences the bigger change in height (larger magnitude of displacement from equilibrium position).

This is true (key words: larger magnitude of displacement).

Here's my conceptual model: With center of mass in mind, which pendulum will produce the most Kinetic Energy at the bottom of the swing? One in which the arm is longer or shorter? Well, since a pendulum merely cycles between Potential and Kinetic energy (like all Simple Harmonic Motion), a larger production of Kinetic Energy will reflect a larger change in Potential energy.

 

[BerkReviewTeach]

The L will be larger both before and after, which could be larger or smaller than the relative difference in PE for a "shorter" arm.

This is true (key words: larger magnitude of displacement).

Here's my conceptual model: With center of mass in mind, which pendulum will produce the most Kinetic Energy at the bottom of the swing? One in which the arm is longer or shorter? Well, since a pendulum merely cycles between Potential and Kinetic energy (like all Simple Harmonic Motion), a larger production of Kinetic Energy will reflect a larger change in Potential energy.

Hey Phantastic, welcome to SDN. This is a great place to get sage advice and insights into questions. There are some great and insightful answers here.

With that in mind, please don't take this as uninviting, because it's not meant to be. You are wrong here and should rethink your analysis.

If you have a longer L, then the pendulum will sweep a semi-circle of greater radius. Take this to the extremes of starting at 90 degrees to the left and sweeping to 90 degrees on the right, for a 180 degree semi-circle sweep total. The change in height in that case would be the radius of the semi-circle, meaning that the semi-circle of largest radius would experience the greatest change in height during its sweep. This question comes down to looking at the L. Perhaps it can be made easier by rewriting the PE equation to show deltaPE:

deltaPE = mg deltaL (1 - cosine theta).

The theta and m are the same for both systems, so only delta L will impact the change in PE. Bigger L means bigger delta L which ultimately means a bigger delta PE.

You are on the right track comparing KE to PE if you want to determine why a great delta L would lead to a great maximum speed, that would get the right answer too.

 

[Phantastic]

You are wrong here and should rethink your analysis.

Indeed, no offense taken. I think I was using h instead of L when thinking this one over earlier for that potential energy calculation. You're deltaPE equation sums it up.

 

[HopefulOncoDoc]

Try redrawing the two pendulums with just one bob at the center of mass. You'll get two pendulums where one has a greater cable length than the other. The system with the greater cable length will experience a greater change in height from highest point to lowest point.

This can be verified if you consider the potential energy equation where PE = mgL (1 - cosine theta). If L increases, then PE increases, so the change in PE must change too.

Does the BR answer explanation show any pictures or is it just words for this one?

Hey BRTeach thank you so much. I can visualize and understand your explanation much easier. The answer explanation on the test was just words and I couldn't visualize what it was stating.