Conservation of Mechanical Energy for a Rolling Sphere

In summary, the conversation is about a physics problem involving a solid sphere rolling without slipping on a horizontal surface and then on an incline. The question is asking for the total energy of the rolling sphere and the vertical height it reaches on the incline. The key is that it rolls without slipping and the relationship between translational and rotational velocity. The rotational inertia of a solid sphere is also mentioned, and it is stated that mechanical energy is conserved.
  • #1
adstroud
4
0
I have one last question due on my physics homework that is due in a few and no one seems to understand how to do it. Please help :)


A solid sphere of mass 0.595 kg rolls without slipping along a horizontal surface with a translational speed of 5.16 m/s. It comes to an incline that makes an angle of 36 with the horizontal surface. Neglecting energy losses due to friction,

(a) what is the total energy of the rolling sphere?
Im pretty sure that this is a total of the trans. velocity and rotational velocity but I don't know how to get the rotational velocity from the information given.

(b) to what vertical height above the horizontal surface does the sphere rise on the incline?
 
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  • #2
adstroud said:
(a) what is the total energy of the rolling sphere?
Im pretty sure that this is a total of the trans. velocity and rotational velocity but I don't know how to get the rotational velocity from the information given.
The key is that it rolls without slipping. That should tell you the relationship between translational and rotational velocity.

What's the rotational inertia of a solid sphere?
 
  • #3
this should help:

K.E= 1/2 mv^2 ( 1+ k^2/r^2)
 
  • #4
so what is the vertical height it goes on the incline
 
  • #5
adstroud said:
so what is the vertical height it goes on the incline
Hint: Mechanical energy is conserved.
 

What is the "Energy of Rolling Sphere"?

The energy of a rolling sphere refers to the kinetic energy and potential energy it possesses as it moves and rolls on a surface. It is the energy that allows the sphere to keep rolling and overcome any resistance or friction.

What factors affect the energy of a rolling sphere?

The energy of a rolling sphere is affected by its mass, radius, velocity, and the surface it is rolling on. These factors determine the amount of kinetic and potential energy the sphere has.

How is the energy of a rolling sphere calculated?

The energy of a rolling sphere is calculated using the formula E = 1/2mv^2 + mgh, where E is the total energy, m is the mass of the sphere, v is the velocity, g is the acceleration due to gravity, and h is the height of the sphere's center of mass.

Can the energy of a rolling sphere be converted into other forms of energy?

Yes, the energy of a rolling sphere can be converted into other forms of energy such as heat, sound, or work. This is because the energy of the sphere is constantly being transferred and transformed due to friction and other external forces.

How does the energy of a rolling sphere relate to its motion?

The energy of a rolling sphere is directly related to its motion. As the sphere rolls, its kinetic energy increases, and as it moves to a higher position, its potential energy increases. This energy is then converted back into kinetic energy as the sphere rolls down a slope or encounters other forces.

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