Question

A 106 kg clock initially at rest on a horizontal floor requires a 670 N horizontal force to set it in motion. After the clock is in motion, a horizontal force of 557 N keeps it moving with a constant velocity.

a) what is the μs between the clock and the floor?.70
b) what is the μk between the clock and the floor?

Answer 1

a)
`\mu_s=0.65`

b)
`\mu_k=0.54`

Step-by-step explanation:

Static friction is when the body is at rest or is about to move while kinetic friction is when the body is already in motion. According to Newton's second law:

`\sum F_y:N=mg\\\sum F_x:F_f=F_x`

a) In this case, the static friction must be equal to the horizontal force to set the clock in motion:

`F_f=\mu_sN=\mu_smg\\\mu_smg=F_x\\\mu_s=(F_x)/(mg)\\\mu_s=(670)/(106kg(9.8(m)/(s^2)))\\\mu_s=0.65`

b) In this case, the kinetic friction is equal to the horizontal force that keep the clock moving with constant velocity:

`\mu_kmg=F_x'\\\mu_k=(F_x')/(mg)\\\mu_k=(557)/(106kg(9.8(m)/(s^2)))\\\mu_k=0.54`