Question

the solid homogeneous cylinder is released form rest on the ramp if theta=30 degrees Ms=.2 and Mk=.1, w=15lb, r= 8" determine the

a. magnitude of the acceleration of the mass centered at g

b. the magnitude of the frictional force exerted by the ramp on the cylinder

c. the minimum value of static frictional coefficient Ms to insure pure rolling and no slipping

Answer 1

Here we apply concept of Newton's laws of motion and Newton's laws of rotation.

Anu =15lt Mass = M Radius = 8 O=300 M = 0.2 l = 0.1 free body stiegram . Here N= Normal force f = friction Mg = gravity. H Mg Pla Perpendicular to incline, ay=0 =_=) MK - Mg Cos o zo - a Np = Mg Cao static friction, (fs) man = Ms Nr. Along the incline, <Fx = mase => Mq sino- t =man.

fos fo To ensure Pure ralling, a cm = xr Tret = ) () o = I x = (fs) (r) ung Inna I My z MV2X = () Co =ffs = - Macm - How Alory incline, Mg Sino - fs = M am from o & = Mg sino = 3 fs 5 Mg Sino =lis Mg Cas 0) (3) reusit lente >fus)min = 0.1924 1 0

As Ms = 0.2 s) mir to pure rolling will occur. (a) Macm= Mg (sin o - Ms Coro) a acm = (9.8 m/s2) (Sin 36 - (0-2) (ca 38) - Ccm = 3.2 m/s2 (6) frictional force acting Is My Na = (6.22 (15abf) Con 300 = 2.598 Ibot = 11:6 Newton (c) Ms) min = 0.1924