Highway curves are marked with a suggested speed. if this speed is based on what would be safe in wet weather, estimate the radius of curvaure for a curve marked 50km/h? the coefficient of static friction of rubber on wet concrete is .7, the coefficient of kinetic friction of rubber on wet concrete is .5 .

Radial (aka centripetal) acceleration keeps cars on an unbanked road in a curve. This acceleration is given by



The force required to keep in going in a circle is given by Newton's second law, F=ma.  Here a is the radial acceleration from the above equation, so we get a radial force:



This force is mediated by the friction force between the tires of the car and the road.  For friction force we use the coefficient of friction and the normal force of the road on the car (which will also be the force of the car on the road).  On an unbanked road this is just the weight of the car, mg.  

The question now is, which coefficient of friction to use?  It might surprise you to find that although the car is moving relative to the road, we should use the static coefficient.  To see why this is the case, think about what the wheel's surface is doing as it meets the road.  As a wheel rotates around and comes into contact with the road surface, it's bottom section is moving in a direction opposite to the car's forward movement.  The point that actually touches the road is moving backward at the same speed that the car moves forward and so it is at rest with the street.  If this were not the case, your tires would always be skidding on the road.  (If you're having trouble seeing this, there are plenty of animations of this phenomenon on the internet). Once a car is skidding it is no longer in control and cannot turn like one that is not skidding.

So now the friction force is just



We now have to set these equal and solve for r, the radius of the circle we are traveling in.  Note that mass will cancel and so we don't need to worry about the mass of the cars involved:



Where I have converted the speed to m/s for unit consistency. 

  sequence  is a continuous and distinctive band of  stars  that appears on plots of stellar  color  versus  brightness. these color-magnitude plots are known as  hertzsprung–russell diagramsafter their co-developers,  ejnar hertzsprungand  henry norris russell. stars on this band are known as  main-sequence stars  or  dwarf stars. these are the most numerous true stars in the universe, and include the earth's  sun.after condensation and ignition of a star, it generates  thermal energy  in its dense core region through  nuclear fusion  of  hydrogen  into  helium. during this stage of the star's lifetime, it is located on the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and age. the cores of main-sequence stars are in  hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of  gravitational collapse  from the overlying layers. the strong dependence of the rate of energy generation on temperature and pressure to sustain this balance. energy generated at the core makes its way to the surface and is radiated away at the  photosphere. the energy is carried by either  radiation  or  convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both.the main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. stars below about 1.5 times the  mass of the sun  (1.5  m☉) primarily fuse hydrogen atoms together in a series of stages to form helium, a sequence called the  proton–proton chain. above this mass, in the upper main sequence, the nuclear fusion process mainly uses atoms of  carbon,  nitrogen  and  oxygen  as intermediaries in the  cno cycle  that produces helium from hydrogen atoms. main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. below this mass, stars have cores that are entirely radiative with convective zones near the surface. with decreasing stellar mass, the proportion of the star forming a convective envelope steadily increases. main-sequence stars below 0.4  m☉undergo convection throughout their mass. when core convection does not occur, a helium-rich core develops surrounded by an outer layer of hydrogen.in general, the more massive a star is, the shorter its lifespan on the main sequence. after the hydrogen fuel at the core has been consumed, the star  evolves  away from the main sequence on the hr diagram, into a  supergiant,  red giant, or directly to a  white dwarf.