Solve Curved Track Problem: Find Times & Stop Position

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Homework Help Overview

The problem involves a particle sliding along a curved track with elevated ends and a flat central section. The track has frictionless curved portions and a flat part with a coefficient of kinetic friction. The particle is released from a height, and the discussion revolves around determining the number of oscillations before coming to rest and the final stopping position.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of not having mass in the problem and how it affects the use of the coefficient of friction. There are attempts to apply conservation of energy to find velocity at the bottom of the track. Questions arise about calculating deceleration on the flat part and the relationship between work done by friction and potential energy loss.

Discussion Status

Some participants are exploring different interpretations of the problem, particularly regarding the role of mass and friction. There are indications of attempts to derive relationships between the variables involved, but no consensus has been reached on a complete solution.

Contextual Notes

Participants note the absence of mass in the problem, which raises questions about how to incorporate the coefficient of friction into their calculations. The discussion also reflects on the implications of this missing information for determining deceleration and the final stopping position of the particle.

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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
 
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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...
 
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
 
ahh of course.
 

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