A solid cylinder (disk) and a hollow cylinder are rolling with the same center-o

Question

A solid cylinder (disk) and a hollow cylinder are rolling with the same center-of-mass velocity v = 2 m/s on a level surface towards an incline. Both cylinders have the same radius R and mass M. The moments of inertia are:
Solid cylinder Is = MR2/2
Hollow cylinder Ih = MR2

A solid cylinder (disk) and a hollow cylinder are rolling with the same center-of-mass velocity v = 2 m/s on a level surface towards an incline. Both cylinders have the same radius R and mass M. The moments of inertia are:
Solid cylinder Is = MR2/2
Hollow cylinder Ih = MR2

Explanation / Answer

a)

The kinetic energy is given by:

KE = 0.5 I omega^2

now since the velocity of center of mass and the radius for both are same hence the angular velocity omega will be same.

The translation kinetic energy for both will be same which is 0.5 Mv^2 but the rotational kinetic energy will not because they have different moment of inertia.

b) Conservation of mechanical energy will help in this regard because there is only conservative forces.

c) At maximum heigh the kinetic energy will be zero,

hence Mgh = 0.5 Mv^2 + 0.5 MR^2/2*(v/R)^2 = 0.5 Mv^2+0.25 Mv^2 = 0.75 Mv^2

h = 0.75v^2/g = 0.75*2^2/9.81 = 0.31 m

d) At maximum height the kinetic energy will be zero hence,

Mgh = 0.5 Mv^2 + 0.5 MR^2*(v/R)^2 = 0.5 Mv^2+0.5 Mv^2 = Mv^2

h = v^2/g = 2^2/9.81 = 0.41 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.