F5 PHYSICS (MECHANICS)

1. You have not given under what situation the car turns a corner. I could only provide my answer based on the most simple configuarion, i.e. a car turns a corner on a rough leve road.

Suppose a car of mass m turning a corner of radius r at a speed v. The centripetal force required for turning is provided by friction on the road, then
mv^2/r = Ff -------------------------- (1)
where Ff is the frictional force

For a given car and a given corner, the max speed for turning v(max) is found when the frictional force reaches its max value, i.e. when Ff = uR, where u is the coefficient of friction and R is the normal reaction.

Hence, m[v(max)]^2/r = uR
but R = mg on a level roas, we have, m[v(max)]^2/r = u(mg)
v(max) = square-root[r.u.g] -------------------- (2)
The above equation shows that v(max) is actually independent from the mass of the car.
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2. I don't know what lecture notes you refer to.
From equation (1) above, as far as the frictional force Ff has not yet reached its max value, you could increase both v and r simultaneously.