Which ball has more energy halfway through the track?

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Homework Help Overview

The discussion revolves around two frictionless tracks with equal length bumps, where participants are examining the energy dynamics of two balls moving along these tracks. The original poster questions which ball has more energy halfway through the track, considering they started at the same height.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concepts of kinetic and potential energy, questioning whether the total mechanical energy differs between the two balls at the halfway point. They discuss the implications of velocity on kinetic energy and the relationship between potential energy and total mechanical energy.

Discussion Status

The discussion is ongoing, with participants providing insights into kinetic and potential energy. There is a focus on clarifying the definitions and components of total mechanical energy, and participants are questioning the assumptions made about the energy states of the balls.

Contextual Notes

Participants are considering the effects of gravity and the absence of friction in their analysis, which may influence their understanding of energy changes. There is an emphasis on the conditions under which total mechanical energy can change.

Irfan Nafi
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2 frictionless tracks have equal length bumps with one going up and the other down. Halfway through the track which one has more energy?

Assuming that they started at the same height, I thought that they had the same amount of energy, but since Ball B ends up having a greater velocity at the end of the track wouldn't that mean that it would have a greater amount of kinetic energy. Thank you in advance.
 
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Irfan Nafi said:
View attachment 211212

2 frictionless tracks have equal length bumps with one going up and the other down. Halfway through the track which one has more energy?

Assuming that they started at the same height, I thought that they had the same amount of energy, but since Ball B ends up having a greater velocity at the end of the track wouldn't that mean that it would have a greater amount of kinetic energy. Thank you in advance.

You are right about Kinetic Energy part .But does the question ask about greater KE or greater total mechanical energy ?
 
The overall energy, so it's the greater mechanical energy.
 
Irfan Nafi said:
The overall energy, so it's the greater mechanical energy.

What is total mechanical energy composed of ?
 
Potential and kinetic energy.
 
Potential and kinetic energy.
 
Irfan Nafi said:
Potential and kinetic energy.

KE is greater for ball B but is potential energy also greater for ball B ?

Why do you think total mechanical energy is greater for ball B ?
 
Since it has a greater velocity at the end of the track
 
Irfan Nafi said:
Since it has a greater velocity at the end of the track

I don't understand you . Half way through the track ball B has more KE , but does it have more PE as well ? Only then you can safely conclude that total mechanical energy is greater for B .

Total mechanical energy is changed only when either some external agent is doing work or due to the presence of some frictional/dissipative forces . Gravity is not considered an external agent . It's effect is included in the PE term .

The balls are moving on their own , so it doesn't look as if some external agent is there . Is there any friction on the track ?

What would cause the change in total mechanical energy ?
 
  • #10
Irfan Nafi said:
it has a greater velocity at the end of the track
What is your basis for saying that?
 

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