# Coefficient of dynamic friction

1. Nov 2, 2007

### suspenc3

1. The problem statement, all variables and given/known data

A 4 kg collar C rides along a horizontally rotating arm AB. A spring k connects C to A. The arm AB rotates at a constant rate of 15 rpm. At the illustrated instant r = 1 m, r˙ = 1.1 m/s, and r¨ = 4 m/s2. The coefficient of dynamic friction, μk, is equal to 0.3. What is the magnitude of the total force exerted by the spring on the collar?

2. Relevant equations

$$a=(\ddot {r} -r \dot {\theta}^2)i_R + (2 \dot {r} \dot {\theta} + r \ddot {\theta})i_ {\theta}$$

3. The attempt at a solution

$$\\sumF_r=ma_r=m(\ddot {r} -r \dot {\theta}^2)=-F_s-\mu R$$
$$\\sumF_{\theta}=ma_{\theta}=m(2 \dot {r} \dot {\theta} + r \ddot {\theta})=R$$

Everything is known exepth for $$F_s$$ which is the answer (force on spring), R, and $$\dot {\theta}$$.

$$\dot {\theta}=\frac {rpm*2 \pi}{60} = 1.57$$

I plug in numbers and get R=13.82 and Fs=-10.27

Any help would be appreciated

Last edited: Nov 2, 2007