A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination30o. The co- efficient of static friction µ_(s) = 0.25. (a) How much is the force of friction acting on the cylinder ? (b) What is the work done against friction during rolling ? (c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly ?

A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a pl

1.	A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination30o. The co- efficient of static friction µ_(s) = 0.25. (a) How much is the force of friction acting on the cylinder ? (b) What is the work done against friction during rolling ? (c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly ?
Answer» Solution :Mass of cylinder `m=10kg` Radius of cylinder `r=15cm=0.15m` Angle of inclination `theta=30^(@)` Coefficient of STATIC friction `mu_(S)=0.25` (a) Frictional force exerted on the cylinder PARALLEL to the surface of slope `f=(1)/(3)mgsintheta` `=(1)/(3)xx10xx9.8xxsin30^(@)` `=(1)/(3)xx10xx9.8xx(1)/(2)` `=16.3N` (b) Frictional force exerted on the cylinder perpendicular to the surface of slope = work done against friction force during ROLLING `W=frcos90^(@)` `W=0` (c ) Condition of rolling without SLIDING `mu=(1)/(3)tantheta` `THEREFORE tantheta=3mu` `=3xx0.25` `=0.75` `therefore theta=36^(@)54` `therefore theta~~37^(@)`