A marble that is rolling without slipping approaches a hill

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Homework Help Overview

The problem involves a marble rolling without slipping as it approaches a hill at a speed of 8.5 m/s. Participants are exploring how high the marble will rise under two different conditions: one where the hill is rough enough to prevent slipping and another where the hill is perfectly smooth. The discussion also touches on why the marble reaches different heights despite having the same initial kinetic energy in both scenarios.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conservation of mechanical energy and the need to account for both translational and rotational kinetic energy when analyzing the marble's motion. There are questions about how to calculate the final height and what energy forms are involved in the process.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting the original poster to consider different aspects of the problem. Some guidance has been offered regarding the conservation of energy and the distinction between the two cases, but no consensus has been reached on the final approach or solution.

Contextual Notes

Participants note that the problem requires understanding the effects of rotational motion and the implications of different types of hills on the marble's energy conversion. There is also an acknowledgment of the original poster's uncertainty about their initial approach and calculations.

Kellyn24
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Homework Statement


A marble that is rolling without slipping approaches a hill at 8.5 m/s. How high vertically will the marble go under these circumstances:

If the hill is rough enough to prevent any slipping?
If the hill is perfectly smooth?

Why does the marble rise to different heights when it had the same initial kinetic energy in both cases?

Homework Equations


ME=KE+PE
KE=1/2mv^2+mgh
PE=mgh

The Attempt at a Solution


KE(initial)=1/2(8.5)^2+9.8(0)=144.5
I have no idea how to solve for final or even if that's what to do next.
PE(initial)=0
I'm not sure how to solve final without knowing the height for sure.
Like, I said earlier I don't even know if this is the correct start to solve this.
 
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Kellyn24 said:

Homework Statement


A marble that is rolling without slipping approaches a hill at 8.5 m/s. How high vertically will the marble go under these circumstances:

If the hill is rough enough to prevent any slipping?
If the hill is perfectly smooth?

Why does the marble rise to different heights when it had the same initial kinetic energy in both cases?

Homework Equations


ME=KE+PE
KE=1/2mv^2+mgh
PE=mgh

The Attempt at a Solution


KE(initial)=1/2(8.5)^2+9.8(0)=144.5
I have no idea how to solve for final or even if that's what to do next.
PE(initial)=0
I'm not sure how to solve final without knowing the height for sure.
Like, I said earlier I don't even know if this is the correct start to solve this.
The marble rolls, that means it rotates about its centre. You have to take the rotational energy into account in addition to the translational kinetic energy.
 
Kellyn24 said:
KE=1/2mv^2+mgh
No, try again.
Kellyn24 said:
KE(initial)=1/2(8.5)^2
What's missing on the right?
Kellyn24 said:
I'm not sure how to solve final without knowing the height for sure.
The height is what you are trying to find. What is conserved?
 
In the first case, all of its initial KE (linear KE + rotating KE), ends up as PE
In the second case. only the linear KE gets converted, and the marble is still rotating at the original rate when it stops up the hill
 
dean barry said:
In the first case, ...
Dean, please give the OP a bit more chance to get there with hints.
 
my apologies
 

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