Solve Curved Track Problem: Find Times & Stop Position

[naphiefx]

A small particle slides along a track with elevated ends and a flat central part. The flat part has a length L = 0.40 m. The curved portions of the track are frictionless, but for the flat part the coefficient of kinetic friction is 0.12. The particle is releases from top of the track, which has a height of 0.90m. Find:

a) How many times the particle moves back and forth before coming to rest.

b) Where does it finally stop?

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There is no mass in this problem. How do I solve it when there is no mass? I've only gotten as far as solving for V when the particle reaches the bottom of one side of the track with the conservation of energy.

mgh=1/2mv^2

V = 17.64 m/s

 

[tyco05]

you forgot to take your square root for starters. - recheck your calculation

Hmmm... but without the mass, you can't use the coefficient of friction. So we don't know what the deceleration will be across the flat part of the track...

 

[naphiefx]

Thanks for the reply Tyco!

I got it!

Have to do work done by friction = loss of potential

mew m g x = m g h since Vf = 0

x = h / mew = 7.5m

7.5M/.4M = 18.75 Oscillations

.75 * .4 = .3L - Where it stops on the track

 

[tyco05]

ahh of course.