Some questions about terminology

[AndyCh]

I thought this would be the most logical way to post this, but give me some grace if it is not because this is my first time posting on this site (then relinquish the grace and tell me how to do it properly haha).

First: When a physics problem says "sliding past point P" does that mean it stops after reaching point P, or slides an arbitrary amount past point P?

Second: Is this equation correct?

ΔTE = μmgt

Where TE is thermal energy (ΔTE is heat), μ is the coefficient of friction, g is the local gravity, and t is time

assuming there is no heat transferred to the 'track' (that which the object whose mass and thermal energy is in question is sliding upon) or the air surrounding.

 

[Simon Bridge]

I thought this would be the most logical way to post this, but give me some grace if it is not because this is my first time posting on this site (then relinquish the grace and tell me how to do it properly haha).

First: When a physics problem says "sliding past point P" does that mean it stops after reaching point P, or slides an arbitrary amount past point P?

It just means that it does not stop at point P.

Second: Is this equation correct?

ΔTE = μmgt

Where TE is thermal energy (ΔTE is heat), μ is the coefficient of friction, g is the local gravity, and t is time

Depends, what is it supposed to tell you and under what circumstances?

Looks like you are assuming sliding with friction along a horizontal, flat, surface and that all the energy dissipated by the friction ends up as heat in whatever is sliding. Then it does not look right no. How did you derive it?

Note: work is change in energy is force times distance, not force times time.

 

[CWatters]

Context is everything. For example if the problem said something like "calculate the minimum initial velocity so that the ice puck just slides past point P" then you would base your calculations assuming it stops immediately after P.

Have you got an example problem?

 

[AndyCh]

I didn't really derive it with any particular technique, I just thought it made sense.
How would I calculate the addition of thermal energy to an object in this situation then:

An object with mass m and initial velocity v slides across a track. The friction coefficient between the object and the track is μ. This takes place on the surface of earth.
It is assumed that no heat is transferred to the track, or air surrounding.

 

[jbriggs444]

I
An object with mass m and initial velocity v slides across a track. The friction coefficient between the object and the track is μ. This takes place on the surface of earth.
It is assumed that no heat is transferred to the track, or air surrounding.

Hint: conservation of energy. You have a fixed input of kinetic energy.

 

[AndyCh]

Hint: conservation of energy. You have a fixed input of kinetic energy.

So I would calculate potential and kinetic energy in the system, then subtract that from the total input of kinetic energy to get the remainder as heat!

 

[Simon Bridge]

I didn't really derive it with any particular technique, I just thought it made sense.

How do you know it makes sense if you did not derive it?

How would I calculate the addition of thermal energy to an object in this situation then:
An object with mass m and initial velocity v slides across a track. The friction coefficient between the object and the track is μ. This takes place on the surface of earth.
It is assumed that no heat is transferred to the track, or air surrounding.

I would use my understanding of:
Free body diagram + Newton's Laws.
Work-energy theorem.
suvat equations.

So I would calculate potential and kinetic energy in the system, then subtract that from the total input of kinetic energy to get the remainder as heat!

... did you try that?