An object with a mass of $9 k g$ $9 kg$ is lying still on a surface and is compressing a horizontal spring by $\frac{2}{3} m$ $2/3 m$ . If the spring's constant is $4 \frac{k g}{s^{2}}$ $4 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2017-05-20T16:33:29

The coefficient of static friction is $= 0.03$ $=0.03$

The coefficient of static friction is

$μ_{s} = \frac{F_{r}}{N}$ $mu_s=F_r/N$

$F_{r} = k \cdot x$ $F_r=k*x$

The spring constant is $k = 4 k g s^{- 2}$ $k=4kgs^-2$

The compression is $x = \frac{2}{3} m$ $x=2/3m$

Therefore,

$F_{r} = 4 \cdot \frac{2}{3} = \frac{8}{3} N$ $F_r=4*2/3=8/3N$

The normal force is

$N = m g = 9 g N$ $N=mg=9gN$

The coefficient of static friction is

$F_{r} = \frac{\frac{8}{3}}{9 g} = 0.03$ $F_r=(8/3)/(9g)=0.03$

An object with a mass of 9kg 9 kg is lying still on a surface and is compressing a horizontal spring by 23m2/3 m. If the spring's constant is 4kgs2 4 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?