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

[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

 

[haruspex]

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?

 

[fdajkffk]

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.

 

[haruspex]

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?

 

[Nickie]

for your help!

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!