If you know the coefficient of friction how do you find the maximum velocity to maintain a circular path at a given radius?

Answer 1

say mass(m) = 10 kg, radius(r) = 10 m, say friction coefficient = 0.5

force to break friction = 10 * 0.5 = 5 kgf = say 50 n

to find acceleration required to produce this force use f=m*a, shuffle to a = f / m

so a = 50 / 10 = 5 (m/s)/s, install in a = v^2 / r, so 5 = v^2 / 10,

so 10 * 5 = v^2, so sq. root 50 = v, so v = 7.07 metres / second

if friction coefficient and radius remain the same, altering the mass wont alter the velocity at breakaway point

Answer 2

To find the maximum velocity to maintain a circular path at a given radius knowing the coefficient of friction, you can use the centripetal force equation: ( F_c = m \cdot v^2 / r ), where ( F_c ) is the centripetal force, ( m ) is the mass of the object, ( v ) is the velocity, and ( r ) is the radius of the circular path. The maximum velocity can be found when the centripetal force is equal to the maximum frictional force, ( F_{friction} = \mu_s \cdot m \cdot g ), where ( \mu_s ) is the coefficient of static friction and ( g ) is the acceleration due to gravity. By setting these two forces equal to each other, you can solve for the maximum velocity.