Question

A cylinder of mass M and radius R is initially at rest on a horizontal surface where there is some unknown friction. At 0=t it is pulled by a horizontal force 4 Mg F = and starts to roll without slipping. ( 2 2 1 MRI C = and g acts down).

a- Find the linear acceleration a of the centre of the cylinder (in terms of g).



b- Find the coefficient of friction
 (in terms of given quantities).

  

c- Find the total kinetic energy K of the cylinder at time t (in terms of given quantities).

Answer 1

a. Horizontal force on the cylinder F= 4Mg

Now from Newton's second law of motion

F - Mg = Ma , where a = acceleration  

or , a =( F - Mg)/ M

Since F = 4Mg

So, a = (4Mg - Mg)/M

= (4- ) g

b.Also, = (F- Ma)/Mg

= (4Mg - Ma)/ Mg

= (4 - a/g)

c. Total kinetic energy of the cylinder is

K = 1/2 MV^2 + 1/2 Iw^2

= 1/2 MV^2 + 1/4 M(Rw)^2

= 1/2 MV^2 + 1/4 MV^2

= 3/4 MV^2