An object with a mass of $16 k g$ $16 kg$ is lying still on a surface and is compressing a horizontal spring by $\frac{5}{6} m$ $5/6 m$ . If the spring's constant is $15 \frac{k g}{s^{2}}$ $15 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2018-03-05T07:02:26

The coefficient of static friction is $= 0.08$ $=0.08$

The mass is $m = 16 k g$ $m=16kg$

The compression of the spring is $x = \frac{5}{6} m$ $x=5/6m$

The spring constant is $k = 15 k g s^{- 2}$ $k=15kgs^-2$

The reaction of the spring is $R = k x = 15 \cdot \frac{5}{6} = 12.5 N$ $R=kx=15*5/6=12.5N$

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

The normal reaction of the object is

$N = m g = 16 \cdot 9.8 = 156.8 N$ $N=mg=16*9.8=156.8N$

The coefficient of static friction is

$μ_{s} = \frac{R}{N} = \frac{12.5}{156.8} = 0.08$ $mu_s=R/N=12.5/156.8=0.08$

An object with a mass of 16kg16 kg is lying still on a surface and is compressing a horizontal spring by 56m5/6 m. If the spring's constant is 15kgs215 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?