What Is the Minimum Coefficient of Friction Required to Navigate a Curve Safely?

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To determine the minimum coefficient of friction required for a car to safely navigate a curve with a radius of 260 m at a speed of 18.0 m/s, the centripetal force must equal the frictional force. The centripetal force is calculated using the formula v²/R, while the frictional force is μ*mg, where μ is the coefficient of friction and mg is the normal force. By equating these forces, the equation μ*mg = mv²/R can be simplified to find μ, as mass (m) cancels out. The discussion emphasizes the importance of understanding the relationship between centripetal and frictional forces in solving the problem. Ultimately, this analysis leads to the calculation of the required coefficient of friction for safe navigation of the curve.
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Homework Statement


A flat (unbanked) curve on a highway has a radius of 260 m. A car rounds the curve at a speed of 18.0 m/s . What is the minimum coefficient of friction that will prevent sliding?


Homework Equations



A= v2/R I got the acceleration but the problem does not give the mass for caluculating the normal force

The Attempt at a Solution


1.246 m/s is what I got for the acceleration after that I do not know what I should be doing.
 
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Hi reticpythons, welcome to PF.
The car rounds the curve due to the centripetal force provided by the frictional force.
write down the expression for both and equate them to get the required result.
 
the centripital force is v2/R but I can not think of what i need to equate it to Fnet= Fn-fk=ma but I do not have mass or I might be totally spacing something I should know but I am looking through my notes and can not find or think of anything
 
reticpythons said:
the centripital force is v2/R but I can not think of what i need to equate it to Fnet= Fn-fk=ma but I do not have mass or I might be totally spacing something I should know but I am looking through my notes and can not find or think of anything
Normal force is mg and frictional force is μ*mg.
Centripetal force is m*v^2/r. Frictional force provides centripetal force to the car to go round the curve without skidding.
Equate them to find μ.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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