A marble that is rolling without slipping approaches a hill

AI Thread Summary
A marble rolling without slipping at 8.5 m/s will reach different heights on a hill depending on the hill's surface. If the hill is rough, both translational and rotational kinetic energy contribute to potential energy, allowing the marble to rise higher. Conversely, on a smooth hill, only translational kinetic energy is converted to potential energy, resulting in a lower height. The discussion emphasizes the importance of considering both forms of kinetic energy in solving the problem. Understanding energy conservation is key to determining the marble's maximum height in each scenario.
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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