Question

Problem 2 The uniform disk shown below has a weight of 200 pounds and a radius r = 16 inches. If the coefficient of static friction between the disk and ground is 0.35, determine the largest force P that can be applied before the disk slips. Show complete free body diagram and all work P

Answer 1

6 Anst Weight of the disc (W) = 200 pou ing = 200 found force It is weight not mass W Radius 'n 46 inch. coefficient of friction between the disc and ground in 0.35. M = 0.35. Free body diagram of the disc - N = normal reaction force due to the ground f = frictional force Wong - Frictional force is towards left. The centre of the disc decelerates a so the friction should be opposite to its velocity the - The normal force (N) don not pass through the centre, it is shifted towards right because the front part pushes the table

6 the centre ma a bit more strongly than the back part. Let the linear acceleration of the disc is a. so the equation for the linear motion of of may is P- from free body diagram) The disc rolls without slipping its angular acceleration about the centre is a so the motion is four from t= 12) T= Torque I = moment of inertia Idisca mu? We know p- of ftma Patlains its manimum value when enimum value when if attains equation of mu ma 2 its maximum value. Inex = limiting friction Ming After that Kinetic friction starts and the disc starts slipping, fmax 0.35x ng 70 Pound fone = 0.35x200

Date Page f = 70 pounds force ma 2f 2 P = ft ma p = f +: 2f 3x70 = 3f 270 Pound force P So maximum force (P.) that can be applied before the disc slips is 210 found force,