Question

A rubber toy duck is at rest on an inclined plane. When the angle of inclination of the plane is increased to 36.0°, the toy duck begins to slide down the incline. Then, when the angle is decreased to 29.0°, the speed of the toy duck is constant. What are the coefficients of static and kinetic friction between the toy duck and the incline?

Answer 1

toy begins to slide when the plane is at an angle of 36.0°

at this point the toy has just overcome the static friction

`f_s = \mu_s N`

`f_s = \mu_s mgcos \theta`

since toy begins to slide

`f_s = mgsin \theta`

now on comparing

`mgsin \theta = \mu_s mgcos \theta`

`\mu_s = tan \theta`

`\mu_s = tan (36^0)`

`\mu_s = 0.726`

as the body is moving at constant velocity acceleration will be zero

so now,

`m g sin \theta - f_k = ma`

`m g sin \theta - \mu_k mg cos\theta = 0`

`\mu_k = tan \theta`

`\mu_k = tan (29^0)`

`\mu_k = 0.554`