Which ball has more energy halfway through the track?

[Irfan Nafi]

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.

 

[conscience]

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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.

You are right about Kinetic Energy part .But does the question ask about greater KE or greater total mechanical energy ?

 

[Irfan Nafi]

The overall energy, so it's the greater mechanical energy.

 

[conscience]

The overall energy, so it's the greater mechanical energy.

What is total mechanical energy composed of ?

 

[Irfan Nafi]

Potential and kinetic energy.

 

[Irfan Nafi]

Potential and kinetic energy.

 

[conscience]

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 ?

 

[Irfan Nafi]

Since it has a greater velocity at the end of the track

 

[conscience]

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 ?

 

[haruspex]

it has a greater velocity at the end of the track

What is your basis for saying that?