Roller coaster friction project help

[lidomonkee]

I have a group depending on me.. and I have no idea where to begin with these problems... they're additional calculations connected with a rollercoaster project we're doing... our average friction is .0212 N if that is needed... someone please direct me to some solution you have no idea how much I would appreciate it..

i. if the spring constant is 2000 N/m, how far will the spring have to compress to bring the caoster to a stop? (Assume the weight of the coaster and passengers to be 45,000 N)

ii. If the spring dissipates half the available energy as heat, how far will your ride go (after released by the spring) before it stops or begins to roll foward? Don't forget friction.

 

[Diane_]

Do energy balances on them. For instance, in your first problem, you'll be converting the kinetic energy of the roller coaster into potential energy in the spring. If you neglect losses due to friction, then you can set the one equal to the other and solve. I presume you know how to calculate kinetic energy - there should be an equation in your book for calculating the energy stored in a spring. After dealing with kinetic energy, it will look very familiar.

Now, the problem says not to neglect friction. Fortunately, once you know what you're doing, it's relatively easy to put it back in. You'll do the same energy balance, only this time the kinetic energy of the roller coaster is going both into energy in the spring and into work done by friction. Remember the definition of work - it works with friction, too. Add in that term and you'll have a quadratic, which you can then solve.

After finishing part i, part ii should be pretty easy. Same general idea there.

Is that sufficient?

 

[lidomonkee]

I think so.. so KE = EPE + Heat -> 1/2mv^2 = 1/2kx^2 + Ff*d

and I'm solving for x.. right?