Understanding the Relationship between Work and Power in Accelerating Objects

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Discussion Overview

The discussion revolves around the relationship between work and power in the context of accelerating objects. Participants explore how varying acceleration and time affect the calculations of work and power, examining both theoretical and practical implications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant calculates the work done on a 1kg mass accelerated at 1m/s² over 10m as 10J, questioning the relationship between work, power, and time.
  • Another participant suggests that to vary power while keeping work constant, one could apply a different force over a longer distance, thus changing the time taken.
  • It is noted that if acceleration is held constant, the time cannot be changed, leading to a discussion about instantaneous versus average power.
  • Participants clarify that while force remains constant, velocity changes, which affects power calculations, as power is defined as force multiplied by velocity.
  • One participant acknowledges the correction regarding the relationship between power and velocity, indicating a refinement of understanding.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of work and power, but there is some contention regarding how varying acceleration and time interact in practical scenarios. The discussion remains unresolved in terms of the implications of these relationships.

Contextual Notes

Participants express uncertainty about the implications of constant acceleration on time and power calculations, indicating a need for further exploration of these concepts.

Who May Find This Useful

This discussion may be useful for individuals interested in the principles of mechanics, particularly those exploring the concepts of work, power, and acceleration in physics.

TheLaw
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This isn't homework. I've been thinking.

If I have say a 1kg mass and I want to accelerate it at 1m/s^2 for 10m, I would calculate the work to be done as 10J.

Force = 1kg x 1m/s^2 = 1N
Work = 1N x 10m = 10J

I hope that is correct so far.

But what confuses me is power. Power is work/time, but how could I possibly alter the amount of time it takes for me to accelerate a mass for a certain distance? Wouldn't time be constant?

Is it possible for me to accelerate the mass at 1m/s^2 and then to reach 10m with different amount of times?

Thanks a lot.
 
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No, because you're holding the acceleration constant. What you need to do is hold the work done constant, but vary the time taken. For example, you could similarly do 10J of work by pushing it with a force of 0.5N for 20m, which will give you the same final KE, the same work done, but a different time (and thus a different average power).
 
In your setup, where you have the acceleration specified, you can't change the time.

But that is not the main point. The main point is that power, like velocity, can be calculated between two points very close to each other, so you get an instantaneous value.

In your example, the acceleration (and force) is constant, so the instantaneous power is also constant and is equal to the average power.

However, one could equally move the mass with 10 m/s^2 for the first one meter, and then let the mass slide by inertia for the rest of the distance. Average power would then be different, and, more importantly, the instantaneous power during the first meter would be (much) greater than the average power, while the instantaneous power in the second segment would be zero.
 
voko said:
In your example, the acceleration (and force) is constant, so the instantaneous power is also constant and is equal to the average power.

The force is constant, but velocity is not. Power = force multiplied by velocity.
 
jbriggs444 said:
The force is constant, but velocity is not. Power = force multiplied by velocity.

Indeed. Thanks for correcting that.
 
Well thank you very much. That helped a lot.
 

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