Calculating Distance on a Rollercoaster Using Impulse Method

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The discussion focuses on calculating the average force lost to friction on a rollercoaster model using energy and impulse methods. The user has gathered data on speeds, distances, and accelerations but struggles to determine the distance needed to apply the equation W=F x d for calculating force. It is noted that the energy lost to friction is a more straightforward metric than trying to find the variable friction force. Suggestions include measuring the track directly and utilizing impulse calculations with time and velocity changes to estimate average friction. Ultimately, incorporating time and impulse can provide a pathway to solving for the average force of friction without needing a constant acceleration.
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I am doing a project and one of the questions is to find the average force lost to friction. We measured a ball going down a "roller coaster" (it had 2 humps on it). WE have all the speeds and distances and accelerations, Now i calculated the energy lost to friction by taking the initial gravitational energy and subtracting the gravitational energy and kintetic energy after the first drop. So now I have the W in W=F x d but I can't figure out how to get the distance. Is there a way to calculate it or do I have to go measure it? It doesn't have a constant acceleration so I can't think of how I could calculate it.
 
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You can't really find the "force" lost to friction, since the force isn't conserved or anything nice like that. The energy lost to friction is a much nicer answer.
 
The friction also is very unlikely to be constant. If you want to figure out average friction, you might want to try using time. Getting the distance will involve measuring the track.
 
Nate that is what I am supposed to find, the Average force of friction. But I don't know what to do because don't i need a distance to use the equation W=F x d to solve for F?

I do have the times but i can not figure out how to encorporate them to find the average force of friction.
 
Well, if it's a physical experiment you should probably pull out the measuring tape.
 
What about using impulse, if you have the time and initial and final velocities? Then F(ave)*t = m*(Vf-Vi).
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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