# General Equation about Energy lost due to Friction

• Quantumm
In summary, the conversation discusses finding a generalized equation for the energy lost per meter of track in a marble and track lab. The suggested equation is PEi + KEi + WEi(friction) = KEf + PEf + WEf, and the solution involves finding the difference between the final velocity with and without friction. The conversation also mentions using basic definitions to calculate the energy lost due to friction and encourages exploring and playing with equations to understand physics better.
Quantumm

## Homework Statement

The statement below arises from a marble and track lab, and I'm enthralled to figure out a generalized equation ( variables only ) for energy lost per meter of track. Track is 12 feet long, but can be curved for hills and loops.
Using a small section of track and marble, determine the average energy lost per meter of track.
The track has 2 loops and 2 hills, and starts at a certain height with potential energy only.

## Homework Equations

PEi + KEi + WEi(friction) = KEf + PEf + WEf

## The Attempt at a Solution

1. KE = PE - WE

2. KE = PE - μ*m*g*x(distance)

3. 1/2mv^2 = mgh - ( μ * m * g * x)

4. v^2 = 2(g * initial height) - (μ * g * x)

5. v = √(2*g*h - (μ * g * x))

6. The answer above is final velocity and you can plug that into 1/2mv^2 and compare the energy to the amount it would be without friction v = √(2gh) and find the difference between the two, which in my theory would give the average amount of energy lost per meter.

7. I'm just confused if this is the right solution or even the right direction to go with this problem.

Well, the situation that you're analyzing isn't exactly general (it's a specific case of a body starting from rest at a certain height and then falling down a ramp). However, simply from the definition of work you should be able to find the energy lost due to friction. I'm assuming you don't know calc, so we'll just use basic definitions here:
W=F•∆x=µmg∆x. That's it. You basically knew it already, though :), but just hadn't realized. The energy lost due to friction is just that! If you plug formula #5 into the kinetic energy term and subtract the regular kinetic energy term with no friction, you'll find a result that agrees, which is still pretty beautiful. Love your initiative and the fact that you tried to go deeper into this, that's the best way to learn physics (in my opinion)- look at the equations yourself, play around with them a little, and try to derive some results yourself. Hope this helped :)

## What is the general equation for calculating energy lost due to friction?

The general equation for calculating energy lost due to friction is E = μNΔx, where E represents the energy lost, μ is the coefficient of friction, N is the normal force, and Δx is the displacement.

## How does friction affect the amount of energy lost?

Friction always causes a loss of energy, as it converts kinetic energy into heat. The amount of energy lost due to friction depends on factors such as the coefficient of friction, the normal force, and the distance over which the force is applied.

## What is the relationship between the coefficient of friction and energy lost?

The coefficient of friction is directly proportional to the amount of energy lost due to friction. This means that as the coefficient of friction increases, so does the energy lost. This is because a higher coefficient of friction indicates a greater resistance to motion, resulting in more energy being converted into heat.

## Can friction ever be beneficial in terms of energy loss?

While friction is generally seen as a negative force due to the energy lost, it can also be beneficial in certain situations. For example, friction is essential for stopping a moving object, such as a car, and preventing it from continuously expending energy. Friction is also necessary for some everyday tasks, such as walking, as it provides the necessary traction to move forward.

## How can the amount of energy lost due to friction be reduced?

The amount of energy lost due to friction can be reduced by using lubricants, such as oil or grease, to reduce the coefficient of friction between two surfaces. Additionally, smoother surfaces and proper maintenance can also help reduce the amount of energy lost due to friction.

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