A marble that is rolling without slipping approaches a hill

In summary: I was just trying to helpIn summary, the marble rolling without slipping with an initial velocity of 8.5 m/s will reach different heights depending on whether the hill is rough enough to prevent slipping or perfectly smooth. This is due to the conservation of energy, where in the first case all of the initial kinetic energy (linear and rotational) is converted to potential energy, while in the second case only the linear kinetic energy is converted and the marble maintains its original rotation rate. To solve for the final height, the equations for kinetic energy and potential energy must be used, taking into account the rotational energy in the first case.
  • #1
Kellyn24
1
0

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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  • #2
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.
 
  • #3
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?
 
  • #4
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
 
  • #5
dean barry said:
In the first case, ...
Dean, please give the OP a bit more chance to get there with hints.
 
  • #6
my apologies
 

Related to A marble that is rolling without slipping approaches a hill

What is the concept of "rolling without slipping"?

Rolling without slipping refers to the motion of a round object, such as a marble, where it is both rotating and moving in a straight line without any slipping or sliding. In this type of motion, the point of contact between the object and the surface it is rolling on is always at rest.

How does a marble rolling without slipping approach a hill?

A marble rolling without slipping will approach a hill by maintaining a constant speed and rotating at a constant angular velocity. As the slope of the hill increases, the marble will experience a torque due to gravity, causing it to accelerate down the hill. However, the friction between the marble and the surface will also increase, preventing slipping and allowing the marble to continue rolling without changing its speed or direction.

What factors affect the motion of a marble rolling without slipping?

The motion of a marble rolling without slipping is affected by several factors, including the mass and radius of the marble, the slope and surface of the hill, and the coefficient of friction between the marble and the surface. These factors determine the magnitude of the torque and friction acting on the marble, which ultimately determines its acceleration and motion.

Can a marble rolling without slipping ever stop or change direction?

Yes, a marble rolling without slipping can stop or change direction if an external force is applied, such as a push or a change in the slope of the surface. In these cases, the torque and friction acting on the marble will change, causing its motion to change accordingly. However, as long as there are no external forces, the marble will continue to roll without slipping in a straight line.

How does the motion of a marble rolling without slipping differ from that of a marble sliding without friction?

The main difference between a marble rolling without slipping and a marble sliding without friction is that in the former, the point of contact between the marble and the surface is always at rest, while in the latter, there is no point of contact and the marble is in constant motion. Additionally, rolling without slipping involves both translational and rotational motion, while sliding without friction only involves translational motion.

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