TBR CBT 2 PS Passage II Question 8

[dennis-brodmann]

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This question pertains to the pendulum system of passage II.

Here is the answer explanation as to why D is correct.
Choices A and C can be eliminated immediately, because both of them depict systems in which only one of the two balls is displaced.

I get this since W=∆E. In this case ∆E=m*g*∆h, but m represents total mass.

In choice B (System I), the center of mass when the system is at rest is lower than for choice D (System II), so that point is displaced by a greater distance when System I is moved by the same angular amount as System II. The greater the displacement of the center of mass, the greater the change in the potential energy of the system.

This portion of the explanation confuses me in two ways: (i) because in Choice B, I thought the center of mass was HIGHER since the larger of the two masses is higher and (ii) they called Choice B (System I) but from the passage, this choice would represent System II.

Is there a mislabeling in the answer choices?

 

[stradgirl]

I think it is a typo. Definitely center of mass for system I is lower -> height is lower at 45 degrees -> lower PE -> answer B 🙂

 

[member232]

Although I agree there is a mislabeling in the explanation, I believe the answer is still D.

The center of mass is lower for choice D (compared to choice B) and because they are both displaced by the same angle, the total displacement for Choice D will be greater. Think of the extremes. say the center of mass for "choice b" is at the very top, right where the rope is attached to the bar... the rope is barely displaced.

However, at the end of the rope (when center of mass is lower) the object swings through the maximum distance, and thus will have the greatest change in potential energy.

 

[chocolateislife]

So the center of mass for D where the bigger ball is at the end is greater and as a result Choice D shows greater displacement/greater change in energy? is that right

 

[osprey099]

So the center of mass for D where the bigger ball is at the end is greater and as a result Choice D shows greater displacement/greater change in energy? is that right

D was my answer too. I think TBR messed up on this question cause I really can't see B as the answer..