An object with a mass of $6 k g$ $6 kg$ 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 $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2017-12-24T14:12:32

The coefficient of static friction is $= 0.091$ $=0.091$

The mass is $m = 6 k g$ $m=6kg$

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

The spring constant is $k = 8 k g s^{- 2}$ $k=8kgs^-2$

The reaction of the spring is $R = k x = 8 \cdot \frac{2}{3} = \frac{16}{3} = 5.33 N$ $R=kx=8*2/3=16/3=5.33N$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

The normal reaction of the object is $N = m g = 6 \cdot 9.8 = 58.8 N$ $N=mg=6*9.8=58.8N$

The coefficient of static friction is

$μ_{s} = \frac{R}{N} = \frac{5.33}{58.8} = 0.091$ $mu_s=R/N=5.33/58.8=0.091$

An object with a mass of 6 kg6kg 6 kg is lying still on a surface and is compressing a horizontal spring by 2/3 m23m2/3 m. If the spring's constant is 8 (kg)/s^28kgs2 8 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?