Level Static

Level Static
the coefficient of static friction between the road?

Suppose the coefficient of static friction between the road and the tires on a car is 0.60 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 31.1 m radius?

Depends…is there an embankment (an incline) or is the road flat? I’ll work the problem; so you can plug in what you need to get the answer.

This is a balanced force problem. The forces in balance are friction force F, which is the centripetal force, and the equal but opposite centrifugal force C. As the car is not skidding, the net forces along the raidus of turn R = 31.1 m are f = ma = F – C = 0. In other words, the friction force F = C the centrifugal force when the car is not skidding out into the boonies during the turn.

OK then, F = kN = k mg cos(theta) = mV^2/R = C; where k = .6, m is car mass, theta is the embankment angle, and V = ? the velocity the car is traveling as it goes around the curve. Solve for V = sqrt(kgR cos(theta)); where g ~ 9.81 m/sec^2 on Earth’s surface. If you assume no embankment angle, then set theta = 0. Everything on the RHS is given; now you can do the math.

The physics is this. When there is no acceleration, a body at rest stays at rest and a body at a velocity stays at that velocity. In the car case, the car is at rest along the radius of turn R even though it’s moving forward with tangential velocity V. As there is no acceleration a along the R, we have f = ma = (F – C) = 0, which is why the friction force and centrifugal force are balanced or equal but opposite. And when you solve for V, that V is the velocity that gives the balance to the equation.

Gaiser – Static level

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