Minimum Speed and Coefficient of Friction for a Car on a Circular Race Track

AI Thread Summary
To determine the minimum speed for a car on a circular track with a radius of 340m and a lateral acceleration of 1.2g, the maximum speed was calculated to be 64.17 m/s, equivalent to 141.48 mi/hr. The necessary coefficient of friction to prevent sliding was found using the equation μmg = ma, resulting in a value of 1.24. This analysis confirms that both speed and friction are critical for maintaining stability on a level track. The calculations demonstrate the relationship between speed, radius, and friction in circular motion. Understanding these parameters is essential for safe racing conditions.
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I got a problem: let's say a car traveling around a circular race track of radius 340m. The lateral acceleration of the car is 1.2g. The roadway of the track is level, not banked. What is the mininum speed at which the car can travel on the track without rolling over? What is the minimum coefficient of friction needed between the tires and the roadway so the car will not slide out. I tried my best was unable to solved this one.
 
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What exactly did you try?
 
Well, I know how to solve it now.

First I found the max speed

A=V^2/r where v will equal 64.17 m/s

Change the units into mi/hr which would be 141.48 then plug it
Into mg= ma and get 1.24 as the coefficient of friction
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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