How Does Static Friction Affect Energy Equations in Rolling Motion?

[240rr]

Homework Statement

This question isn't for a specific problem. Just knowledge to approach a series of problems.
It concerns a problem where a uniform sphere rolls smoothly down a ramp at incline theta. There is a static frictional force on the ramp. I can go on to find acceleration I am just unsure as to the role of the force of friction in the energy equations.

Homework Equations

E=KE+U
KE=1/2mv^2
KE=1/2Iw^2

The Attempt at a Solution

I'm just Unsure as to whether The force of static friction should be included in the original energy equation or not:

mgh = 1/2mv^2 + 1/2Iw^2 + Fx ?

 

[240rr]

Did some digging and found an old post

"Even though no work is done by friction, it does cause energy to be transformed into rotational KE. In the ideal case, there would be no loss in mechanical energy. (Of course, in real life there is rolling friction, deformation, etc., which does dissipate mechanical energy.)"

So is this saying that friction creates the rotational kinetic energy? Do I need to include it in the Total Energy equation then as Fx? Still at a bit of a loss. Don't know why I'm having such a hard time picturing what's happening here.

 

[dextrain]

i think as the friction is static therefore no work is done by it, the work done against friction should not be included

 

[240rr]

Thanks for the response. That's what i thought but something my professor told me got me thinking i had to include it in the equation for total energy.

 

[rwisz]

I would approach this problem by first understanding the fundamentals of kinetic energy and how it relates to a rolling sphere on a ramp. Kinetic energy is the energy an object possesses due to its motion, and it is defined by the equation KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

In the case of a rolling sphere on a ramp, we need to consider both translational and rotational kinetic energy. The translational kinetic energy is given by 1/2mv^2, where v is the velocity of the center of mass of the sphere. The rotational kinetic energy is given by 1/2Iw^2, where I is the moment of inertia of the sphere and w is its angular velocity.

Now, in order to find the total energy of the system, we need to consider all the forces acting on the sphere. In this case, there is a static frictional force on the ramp, which is opposing the motion of the sphere. This force does work on the sphere, which means it contributes to the total energy of the system.

Therefore, the correct energy equation for this problem would be:

mgh = 1/2mv^2 + 1/2Iw^2 + Fx

Where Fx is the work done by the static frictional force on the ramp. This force is given by Fx = μN, where μ is the coefficient of static friction and N is the normal force acting on the sphere.

In conclusion, as a scientist, it is important to consider all the forces acting on a system when analyzing its energy. In the case of a rolling sphere on a ramp, the force of static friction does play a role in the energy equations and must be included in order to accurately describe the motion of the sphere.