# Find the energy lost at the collision and the average force of friction

• fdajkffk
In summary, the conversation is discussing the process of determining the energy lost and average force of friction in a roller coaster project. The equations used include conservation of energy and force, and various concepts such as coefficient of restitution and rolling resistance are mentioned. To accurately determine the energy lost during a collision, the coefficient of restitution must be known. The conversation also mentions the possibility of taking into account the moment of inertia of the marble in the calculations.
fdajkffk

## Homework Statement

We have to make a roller coaster for our school project. This coaster starts with a spring. In this coaster, there is a collision. Essentially, I need to find the energy lost at the collision, and the average force of friction.

## Homework Equations

Em1=Em2
W=Fd
F=ma
A=DELTA v/ DELTA t

## The Attempt at a Solution

To find the energy lost, I set:
EM1-Wf=Em2
Em1-Wf=Em2
-Wf=Em2-Em1
-Fdcos180=0.5mv^2-0.5kx^2 (I sub. in the actual measured value of v in)

Is this the correct way to solve for the average force of friction? How do I account for the energy lost during the collision? Would it be included in my Wf? In that case, how would i find the energy lost during the collision?

My other idea for finding the force of friction, is to do a=v/t v= theoretical speed at the end-actual measured speed
Once I find the a value, I can sub it into my F=ma equation to find F. Would this be valid as well?

Thank you

To determine the energy lost you need to know the coefficient of restitution. You can get an upper bound by assuming the colliding masses coalesce and using conservation of momentum.
Where is the friction you're trying to measure? Are the masses on wheels or just sliding?

haruspex said:
To determine the energy lost you need to know the coefficient of restitution. You can get an upper bound by assuming the colliding masses coalesce and using conservation of momentum.
Where is the friction you're trying to measure? Are the masses on wheels or just sliding?

Uhhh the mass is a marble. And I'm trying to measure the average force of friction acting on the marble during its journey. I'm only in 12 U physics so it wouldn't involve that as I haven't learned it yet. I'm pretty sure this should be dealt with from an energy perspective.

fdajkffk said:
Uhhh the mass is a marble. And I'm trying to measure the average force of friction acting on the marble during its journey. I'm only in 12 U physics so it wouldn't involve that as I haven't learned it yet. I'm pretty sure this should be dealt with from an energy perspective.
Since the marble is rolling, it does not lose energy to 'friction'. It will lose energy because of 'rolling resistance' http://en.wikipedia.org/wiki/Rolling_resistance, which is a little different (basically, bouncing up and down on the microscopic scale) and air resistance.
The only way to figure out how much energy is lost when two marbles collide is by knowing or measuring the coefficient of restitution http://en.wikipedia.org/wiki/Coefficient_of_restitution#Speeds_after_impact. Taking the masses to be the same simplifies the equation.
http://hypertextbook.com/facts/2006/restitution.shtml gives a glass marble as 0.66.
You might need to take into account the moment of inertia of the marble. Have you covered that topic?

I would suggest approaching this problem using the conservation of energy principle. In this case, the initial energy (Em1) is stored in the spring and is equal to the final energy (Em2) of the coaster at the end of the track. The energy lost during the collision can be calculated by subtracting the final energy (Em2) from the initial energy (Em1). This energy loss can then be equated to the work done by friction (Wf) and the work done by the spring (Ws). Therefore, the equation would be:

Em1 - Em2 = Wf + Ws

To find the average force of friction, you can use the work-energy theorem (W=Fd) and the average velocity of the coaster. The work done by friction can be calculated by multiplying the average force of friction (Ff) by the distance traveled (d) during the collision. Therefore, the equation would be:

Wf = Ff * d

To find the energy lost during the collision, you can use the work-energy theorem again and the change in velocity during the collision (Δv). The work done by friction can be calculated by multiplying the average force of friction (Ff) by the change in velocity (Δv). Therefore, the equation would be:

Wf = Ff * Δv

To find the average force of friction, you can use the equation F=ma and the average acceleration of the coaster during the collision. This can be calculated by dividing the change in velocity (Δv) by the time taken for the collision (Δt). Therefore, the equation would be:

Ff = m * a

Remember to use the correct units and to consider the direction of the forces involved. I hope this helps in solving your problem!

## 1. How is the energy lost at a collision calculated?

The energy lost at a collision can be calculated by subtracting the final kinetic energy of the objects involved from their initial kinetic energy. This is known as the change in kinetic energy or the kinetic energy lost.

## 2. What factors affect the amount of energy lost at a collision?

The amount of energy lost at a collision is affected by factors such as the mass and velocity of the objects, the angle of collision, and the nature of the surfaces involved (e.g. rough or smooth).

## 3. How is average force of friction calculated?

The average force of friction can be calculated by dividing the force of friction by the surface area over which it acts. This can be represented by the equation F/A, where F is the force of friction and A is the surface area.

## 4. What is the relationship between energy lost at a collision and the average force of friction?

The energy lost at a collision is directly related to the average force of friction. The greater the average force of friction, the more energy will be lost at the collision. This is because the force of friction acts as a resistance to the motion of the objects, thus causing them to lose energy.

## 5. Can the energy lost at a collision and average force of friction be reduced?

Yes, the energy lost at a collision and average force of friction can be reduced by decreasing the mass and velocity of the objects, using smoother surfaces, and decreasing the angle of collision. Additionally, using materials with lower coefficients of friction can also reduce the energy lost at a collision and average force of friction.

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