Comparing Car A & B's Power: Is the Answer 2x or 8x?

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Discussion Overview

The discussion centers around a physics problem comparing the power required by two cars, A and B, with equal mass, as they ascend a hill at different velocities. Car A travels at twice the constant velocity of Car B, prompting participants to analyze how this affects the power output required for each car. The conversation explores concepts of kinetic energy, potential energy, and the relationship between power, work, and time.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant argues that since Car A has twice the velocity of Car B, its kinetic energy is 4 times greater, leading to the conclusion that the power of Car A should be 8 times greater than that of Car B, based on the relationship of power as work over time.
  • Another participant counters that the problem likely refers to the change in potential energy over time, suggesting that kinetic energy does not contribute to the power calculation in this context.
  • A different viewpoint emphasizes that power can also be expressed as the product of force and velocity, indicating that since both cars experience the same force due to their equal mass, Car A's power should only be twice that of Car B due to its doubled velocity.
  • One participant elaborates that the initial kinetic energy of Car A does not affect the power required to ascend the hill, as the energy needed to reach the top remains the same for both cars, regardless of their speeds.
  • There is a mention of real-world factors, such as increased drag for faster cars, which could affect power consumption but are not considered in the problem.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between velocity, kinetic energy, and power, with no consensus reached on whether the power of Car A is 2 times or 8 times that of Car B.

Contextual Notes

The discussion highlights the assumptions made regarding the initial kinetic energy of the cars and the specific conditions of the problem, such as the absence of drag considerations and the lack of clarity on whether the cars start from rest.

imsmooth
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My daughter showed me a question:
Car A and B have equal mass and go up a hill. A has twice the constant velocity of B. Compared to B the power of A is?

I found these answers here which seem to miss the point:
https://answers.yahoo.com/question/index?qid=20070331204221AAtxncN

The answer stated is 2x

However, the KE is 4x greater for car A than B.
Also, the time for car A to go up is 1/2 that of B because of the doubled velocity.

Since Power is work/time shouldn't the power of A be 8x greater than B?
 
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No, I'm not a fan of the wording, but since KE isn't changing, you can't get a power from it. So the problem can only be referring to the change in potential energy over time.
 
Last edited:
You don't need to go through all that KE and work steps.
Power can be also written as
P=F*v (Force times velocity).
As they move with constant velocity, the force should balance the tangential gravity which is the same for both (they have same mass).
So same force, twice the velocity means twice the power.
 
imsmooth said:
However, the KE is 4x greater for car A than B.

The problem doesn't say the car starts from rest so you have to assume they start with KE and 4xKE. That extra speed and KE could have come from the engine some time earlier but the problem is only concerned about the power needed to go up the hill. The initial higher KE could also have come from a previous downward slope. The point is that the KE isn't changing as you go up the hill so it makes no difference to the power required.

Also, the time for car A to go up is 1/2 that of B because of the doubled velocity.

That only reduces how long the extra power has to be delivered for not the amount of power.

If you were asked to calculate the Energy required to get to the top that would be the same in both cases but you might calculate them differently...

Slow car... Energy = Power * Time
Fast car... Energy = 2*Power*Time/2

The fact that both cars use the same energy shouldn't be a surprise because the hill is the same height in both cases. In the real world the faster car would consume more due to increased drag but that wasn't mentioned.

x2 is the correct answer.
 

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