Question

A car starts from rest with a constant tangential acceleration `a_(0)` in a circular path of radius r. At time t, the car kids, find the value of coefficient of friction.

Answer 1

The tangential and centripetal acceleration is provided only by the frictionless force.
`Thus, f sin theta, fcos theta=(mv^(2))/(r)=(m(a_(0)t)^(2))/(r)`
`Rightarrow f=m sqrt(a_(0)^(2)+((a_(o)t)^(4))/(r^(2)))=ma_(0)sqrt(1+a_(0)^(2)t^(4))/(r_(2))=f_("max")`
`mumg=ma_(0) sqrt(1+(a_(0)^(2)t^(4))/(r^(2))) Rightarrow mu=(a_(0))/(g)sqrt(1+(a_(0)^(2)t^(2))/(r^(2)))`