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

Answer:

a) $\mu_s=0.65$

b) $\mu_k=0.54$

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:

$F_f=\mu_sN=\mu_smg\\\mu_smg=F_x\\\mu_s=\frac{F_x}{mg}\\\mu_s=\frac{670}{106kg(9.8\frac{m}{s^2})}\\\mu_s=0.65$

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

$\mu_kmg=F_x'\\\mu_k=\frac{F_x'}{mg}\\\mu_k=\frac{557}{106kg(9.8\frac{m}{s^2})}\\\mu_k=0.54$