Link between increase in Potential energy and the thermal energy lost

[mathbrain9]

Homework Statement

For a rollercoaster if the potential energy is increased (through increasing the height) the speed obviously increases, but what happens to the work done by friction (thermal energy lost) and the average frictional force. I believe it would increase. Am I right?

Relevant Equations

Ek= 1/2mv^2
Ep=mgh

"Heat is the transfer of kinetic energy between molecules. If the velocity is more, the kinetic energy will be more so that the heat is more."

"As an object's speed increases, the drag force from the fluid increases exponentially. For example, when you drive at high speeds, the frictional force of air on the car increases, and fuel economy decreases."

 

[Orodruin]

Your question is not very well specified. Apart from the ”friction” not being very well defined there are a number of other questions about the setup that come to mind (what friction, where, under what interval of the track, how does the track change apart from the drop height being higher?)

Please quote the original formulation of your problem word by word.

 

[mathbrain9]

The friction of the track on the ball during the entirety of the rollercoaster. Also there is no change to the track apart from the dop height being higher.

Original formulation of the problem:

Purpose: To find the following:
1. What is the relationship between the potential energy of a ball bearing at the top of a roller coaster hill and its kinetic energy at the bottom of a hill after a loop de loop (at the point it leaves the track and falls to the floor)?
2. How much heat (thermal energy) was lost due to friction?
3. What is the average frictional force of the track on the ball bearing?

 

[erobz]

The friction of the track on the ball during the entirety of the rollercoaster. Also there is no change to the track apart from the dop height being higher.

Original formulation of the problem:

Purpose: To find the following:
1. What is the relationship between the potential energy of a ball bearing at the top of a roller coaster hill and its kinetic energy at the bottom of a hill after a loop de loop (at the point it leaves the track and falls to the floor)?
2. How much heat (thermal energy) was lost due to friction?
3. What is the average frictional force of the track on the ball bearing?

Surely there must be some relevant dimensions for the rollercoaster height and the loop radius, ect...?

 

[mathbrain9]

It's supposed to be a experimental lab. The lab involves using a plastic roller coaster in which one end is lifted up, while the loop radius only matters in figuring out the length of the entirety of the track which is 4.22 meters.

 

[erobz]

1. What is the relationship between the potential energy of a ball bearing at the top of a roller coaster hill and its kinetic energy at the bottom of a hill after a loop de loop (at the point it leaves the track and falls to the floor)?

So, for the lab you need to determine how much energy it has at the end of the track by measuring something. Are you trying to work out in theory what this measured value should be if no frictional losses are accounted for?

 

[mathbrain9]

yeah by measuring the distance a marble travels after leaving the roller coaster. By using 2D horizontal projectile motion find the horizontal velocity and use it to determine kinetic energy.

 

[erobz]

yeah by measuring the distance a marble travels after leaving the roller coaster. By using 2D horizontal projectile motion find the horizontal velocity and use it to determine kinetic energy.

So, the marble leaves the track and undergoes projectile motion, and you are going to measure the range. Seems like you are potentially introducing more sources of error as this progresses, but if that's what's expected...

So what is your issue with the calculations?

 

[mathbrain9]

The lab was performed by group when I was sick so I wasn't there. On their data they changed the length of the roller coaster with each trial, when the only manipulated variable was supposed to be the height the marble was dropped on the roller coaster. So I was just wondering theoretically without that error they made in the lab, as the height of the drop increased (more potential energy) would the work done by friction, or the thermal energy lost increase, and would the frictional force increase. That was my only concern.

 

[erobz]

The lab was performed by group when I was sick so I wasn't there. On their data they changed the length of the roller coaster with each trial, when the only manipulated variable was supposed to be the height the marble was dropped on the roller coaster. So I was just wondering theoretically without that error they made in the lab, as the height of the drop increased (more potential energy) would the work done by friction, or the thermal energy lost increase, and would the frictional force increase. That was my only concern.

We’ll, changing the height of the roller coaster changes the length.

Anyhow, tell us your thoughts on it. What can you reason out?

 

[mathbrain9]

The plastic roller coaster was like the picture below. You would take the first part of the track and just lift it up at different heights not changing the total length of the track.

 

[erobz]

So you are talking about doing this:

 

[mathbrain9]

That is absolutely correct.

 

[erobz]

That is absolutely correct.

Well, there are going to be "Normal force" dependent forces like "rolling resistance" that may decline in some regions of the track and grow in others. Drag should be larger for the tilted track since I expect larger average velocities over the entire track.

There is probably a reason why this is intended as a lab exercise. Without doing any calculations I expect the normal force dependent friction changes to cancel out, and the drag to grow.

 

[mathbrain9]

These are the calculations they got although while making the mistake of increasing the length of the track. Through the data they made the connection that when increasing the height of the drop, leads to increases in velocity which subsequently would lead to work done by friction (heat loss) and the average frictional force to increase. Their writing is a little messy.

 

[malawi_glenn]

Will the marble roll or slide?

 

[mathbrain9]

The marble will roll.

 

[mathbrain9]

Will the marble roll or slide?

I searched it up and I got an answer saying the coefficient of sliding friction increases with speed, over a wide range of sliding speeds, leading to higher frictional force. Also as there is higher overall friction, the work done by friction would lead to higher amounts of thermal energy (heat). But common sense is telling me that the marble is obviously rolling across the track and not sliding.

 

[haruspex]

I searched it up and I got an answer saying the coefficient of sliding friction increases with speed, over a wide range of sliding speeds, leading to higher frictional force. Also as there is higher overall friction, the work done by friction would lead to higher amounts of thermal energy (heat). But common sense is telling me that the marble is obviously rolling across the track and not sliding.

You need to be careful about the relationship between questions 2 and 3.
Q3 asks about the average frictional force, but most of that will be static friction as the ball accelerates rotationally. Static friction does no net work, so does not contribute to the generation of heat.

Indeed, it is not clear what Q2 intends. When an object rolls, the losses that turn into heat are caused by "rolling resistance". That covers a range of affects:

• axle friction in a wheel (not relevant in this case)
• inelastic deformation of the rolling object
• inelastic deformation of the substrate
• bouncing on a rough surface
• drag

Some writers call it "rolling friction", but a worrying number wrongly just refer to it as "friction".
Drag force does increase with speed, linearly at low speeds, quadratically at higher speeds. I think the others should be constant.

In kinetic friction, the frictional force can increase with speed or decrease with speed, depending on the materials.

 

[malawi_glenn]

But common sense is telling me that the marble is obviously rolling across the track and not sliding.

The marble can also rotate and slide at the same time, but not rolling. It depends on the surface of the marble and the surface of the track, and the angles involved,

This is why you should not do these experiements with spheres and balls and such, unless you can ensure they roll at all instants.

I do essentially the same experiement with my classes, I use a hotwheels track that I have glued on some thin rubber stripes. Then I have a marble made of steel which is coated in some kind of rubber.

 

[mathbrain9]

What would be relevant sources of error for the experiment as there appears to be a lot. I already know human tracking when the ball hits the ground, but I'm not sure of anymore. For why the calculated value is different from the actual value.

This what I wrote so far:

Firstly, was that components of the plastic roller coaster track were inadequately attached. There were sizable gaps between the track at certain segments seemable disassembled by previous groups’ incompetence. For the first couple practice attempts there were even points where the ball would slip off the track particularly at the plastic loop as the attachment pieces were sticking out and not attached properly. That led to overall the velocity of the ball being perhaps lower than it hypothetically should have been due to the inconsistencies in the layout of the track. Another error would be the shape of the track being very bendable. When choosing a height to drop the ball onto the track, we found that the track would bend a lot more in certain test runs; it would end up bending to the point of being in an upright position while other instances would be slanted. This causes a lot of inconsistencies as the curved path drops lower than the slanted path, initially, which increases the velocity at which it travels the majority of the distance. The slanted path drops only slightly, so the ball has to travel the majority of the distance at a lower velocity. That bendability of the track when dropping the ball initially led to many flaws in the data especially in changing the velocity due to the varying shape of the track. The last error would be human error when tracking the distance the ball traveled after leaving the track. Although we had two people seeing where the ball was landing, there were a lot of assumptions made as the ball was surprisingly hard to detect. The distance the ball traveled after leaving the roller coaster was absolutely off by at least a couple centimeters although we made our best attempt at minimizing error, however using the human eye to track exact measurements does have several inherent flaws.

 

[haruspex]

human tracking when the ball hits the ground

Wouldn't you use e.g. a sand floor so that you can see exactly where it landed?

A couple of points I missed before:

"As an object's speed increases, the drag force from the fluid increases exponentially

Nonsense. It's quadratic at most.

2. How much heat (thermal energy) was lost due to friction?

No heat is lost due to friction. Heat may be generated due to kinetic friction, which may or may not then be lost due to conduction etc.
Presumably they mean "How much mechanical work is lost as heat due to friction?"
Even then, as I wrote in post #19, it is very unclear what is meant by that.
Taking it literally (and assuming the ramp is not so steep that the ball partly slides), since the friction is static, none is lost.
If they mean rolling resistance, with that encompassing the list I gave, then you can count all loss of mechanical energy.