Acceleration and friction problem

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Homework Help Overview

The discussion revolves around a physics problem involving a car accelerating on a circular track, focusing on concepts of tangential and centripetal acceleration, friction, and angular velocity. The problem requires participants to analyze the relationships between these concepts as the car moves along the track.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of tangential and centripetal acceleration, with some suggesting alternative methods for finding these values. Questions arise regarding the application of friction formulas and the need for mass in calculations.

Discussion Status

Some participants have provided guidance on the correct formulas to use for tangential and centripetal acceleration. There is acknowledgment of confusion regarding the initial attempts, but progress is noted as participants refine their understanding and calculations. Multiple interpretations of the problem are being explored.

Contextual Notes

Participants express uncertainty due to missing information, such as mass, which complicates the application of certain formulas. There is also a mention of the original poster's unfamiliarity with the concepts involved.

PhilCam
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Homework Statement



A car is on a circular track of radius r=120 m. It accelerates from rest to a speed of 20 m/s in 8 seconds with constant acceleration. At the end of the 8 second the car is next to a marker on the track.

A) Find the ratio of the tangential acceleration to the centripetal acceleration as the car reaches the marker.

B) Find the minimum coefficient of friction between the tires and track's pavement so that the car does not go out of the track at the marker.

C) At the marker the tires are rolling without slipping. The radius of the tires is .25m. Find the angular velocity of the tire at the marker.


The Attempt at a Solution



A) Tangential acceleration = radius x angular acceleration
=120 x 2.5 = 300

Centripetal = radius x angular velocity squared
=120x 20^2=48,00

I am very unfamiliar with these concepts and I know that this answer is not right; however I have read the chapter in the book but I am still unsure on how to solve this portion of the problem using the formulas given.

B) F=(N) (Coeff of friction)
I do not know how to use this formula because a mass was not given to me to solve for force.

C) Well if the radius of the tire is .25 m and the car is going 20 m/s, then I would assume the wheel has an angular velocity of 80 rad/s.

I am really having trouble with this chapter and any help would be appreciated.
 
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Part (a) does not seem to have anything to do with angular velocity or acceleration. The tangential acceleration can be found using a = Δv/Δt.
The centripetal acceleration may be found using a = v²/R.

For (b), you are looking for the "grip" the car needs on the road so that it will not slip. That is, the friction needed to provide the centripetal force. Begin with Ff = Fc.

Part (c) looks correct!
 
Okay I found the correct answer for A. Thank you so much for simplifying, those equations were much less confusing than the ones listed in my textbook.

And then for part B:

Ff = V^2/(g)(r)
Ff = .34

Is this correct?
 
Correct!
 

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