How Does Friction Affect Energy Conservation in Rotational Motion Experiments?

[Painguy]

Homework Statement

We performed a small experiment in class which had us attach a mass to a string which hung on a pulley which led to a rotating object.

We were then told to write down a conservation of energy equation stating that the initial energy is equal to the final energy. We were asked to include kinetic energy (rotational, translational), potential energy, and energy lost due to friction which we found with Tf=f*r.

Homework Equations

The Attempt at a Solution

This is what I have setup so far.

Ui +Kroti +Ktransi=Uf+Krotf +Ktransf +Wf

mgd=.5Iw^2 + .5mv^2 -f

I'm still a little confused about how energy is conserved if we're losing energy due to friction?

After that they ask me to replace every instance of w with v/r and v with 2d/t and try to get the following I=(mr^2)((gt^2/2d)-1-(t^2/(2md))f)

What am I doing wrong here?

 

[haruspex]

mgd=.5Iw^2 + .5mv^2 -f

f is the force of friction? If so, there are two things wrong with the -f term.

 

[Arkavo]

how in the world are you equating torque with energy

 

[Painguy]

f is the force of friction? If so, there are two things wrong with the -f term.

I suppose I should have did f*Δd? I'm not sure what to do here.

 

[Nickie]

I would like to clarify that energy is always conserved in a closed system, meaning that energy cannot be created or destroyed, only transferred or transformed. In this experiment, the initial energy (potential energy + kinetic energy) is equal to the final energy (potential energy + kinetic energy + work done by friction). This is known as the law of conservation of energy.

In your equation, you have correctly accounted for the initial and final energies, but you are missing the work done by friction. The correct equation should be:

Ui + Kroti + Ktransi = Uf + Krotf + Ktransf + Wf

where Wf is the work done by friction, which can be calculated as Wf = f * d (not Tf = f * r). This is because the force of friction is acting along the distance d, not the radius of the pulley.

As for replacing w with v/r and v with 2d/t, these substitutions are valid as long as the rotational and translational velocities are related by v = r * w. This is known as the tangential velocity equation. However, it is important to note that this substitution only works for a specific moment in time and may not hold true for the entire duration of the experiment. It would be more accurate to keep w and v separate in the equation and only use the substitution when necessary.

In the final equation you were asked to derive, it seems like there may be an error in the original equation given, as it does not match the units of the final equation. It would be best to double check the original equation and make sure all units are consistent throughout the calculation.