Question

A solid disk of mass 2 kg and radius 2 m is given a horizontal push of 20N at a point .3 m above its center. a. What is the minimum μs between the disk and the floor to allow rolling without slipping?

Answer 1

`\mu_s=1.0205`

Step-by-step explanation:

Given:

• mass of solid disk,
  `m=2\ kg`

• radius of disk,
  `r=2\ m`

• force of push applied to disk,
  `F=20\ N`

• distance of application of force from the center,
  `s=0.3\ m`

For the condition of no slip the force of static friction must be greater than the applied force so that there is no skidding between the contact surfaces at the contact point.

`\therefore F<f_s`

where:

`f_s` = static frictional force

`\Rightarrow 20<\mu_s* N`

`\Rightarrow 20<\mu_s* m.g`

`\Rightarrow 20<\mu_s* 2* 9.8`

`\mu_s>1.0204`