The Berkeley Review CBT 1 Question 38

[Dirty Harry]

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Hello All who did The Berkeley Review CBT and representatives:

I am not understanding the question regarding the 38 of the perpetual motion machine.

Here's the question with explanation:

38. What design change might increase the time that the machine described in the passage could run before stopping?

A. Submerging the entire machine underwater.
B. Submerging roughly two-thirds of the machine into a liquid that is less viscous than water.
B is the best answer. Any change in the system that decreases the resistance allows the machine to operate for a longer time. The more deeply the machine is submerged into the water, the more resistance it experiences, because water offers more resistance than air. This eliminates choice A. Placing the machine in a less viscous liquid would reduce the resistance on the machine. This makes choice B the best answer. Here is why choices C and D are wrong: Changing the gas in the balloon has no effect, because the gas in the balloon does not itself offer any resistance to the operation of the machine. Only the walls of the balloon offer resistance. The volume of the balloon is the same regardless of the density of the gas it holds, because the volumes of all gases are roughly equal under the same environmental conditions (i.e., at 0˚C and 1.00 atm., the volume of any gas is 22.41 liters). The best answer is B.
C. Filling the balloons with a denser gas.
D. Filling the balloons with a less dense gas.




Am I supposed to know the viscosity equation for this? My thinking was that if there was more resistance, the time needed for the machine to work will increase, not the other way around as the answer explains: Decreased resistance increases the time.

Thank you for taking you time and answering this. I appreciate this.

 

[sp808]

The viscosity equation isn't necessary. The only concept is that introducing a drag force sucks energy out of the system that has a finite amount of energy (because it isn't really a perpetual motion machine), the more drag force, the faster that energy is lost, thus the shorter the operation duration. Yes, the machine moves slower but that's a result of kinetic energy being lost at a higher rate, not because the machine is conserving its energy to run for a longer time. Rethink the casual relationships in this scenario.

 

[Dirty Harry]

Sp808,

Thank you for trying to help me elucidate this problem. So as I am understanding this:

A less viscous fluid will cause a lesser drag force, then slower energy lost and hence longer operation time for choice B to be the answer?

 

[Dirty Harry]

"Yes, the machine moves slower but that's a result of kinetic energy being lost at a higher rate, not because the machine is conserving its energy to run for a longer time."

So the machine is losing energy and hence the fictional apparatus will take longer to operate?

 

[sp808]

No, I said not because of that. It will run for a shorter time because it loses all of its energy faster. An analogous situation is rolling a ball on a surface that has friction. You input a finite amount of energy into rolling the ball, and the total time that the "system" operates is inversely proportional to how rough the surface is, or how much frictional force the ground applies to slow the ball down. So rolling the ball on a smoother surface is equivalent to using a less viscous liquid, because both are reducing the force that is taking kinetic energy away from the ball. Both will allow the ball to roll longer or the machine to run longer.