Question

How come a heavy truck and a small car can both travel safely at the same speed around an icy, banked-curve road? I would think that since mass is increased, normal force is therefore increased, and force of friction is therefore increased. And since the opposing force, the centripetal force, is just v^2/r, if both cars are going the same speed that force is the same. So wouldn't the forces of friction be different?

Similarly, if a driver wants to drive faster and puts some sand bags in his van aiming to increase the force of friction between tires and road, why will that not help? Again, I would think increased mass --> increased normal force --> increased force of friction. I understand that if he's driving faster, then the centripetal force also increases with v, but if he puts a bunch of sand bags in, the force of friction should increase, right?

Answer 1

forcefriction=centripetalforce
mu*mg= mv^2/r

notice mass divides out.
mu*g=v^2/r

mu= v^2/(rg)

Answer 2

Oh gotcha. But how come friction=centripetal force? I thought since net force is towards the center they can't cancel each other out like that...