An object with a mass of $3 k g$ $3 kg$ is lying on a surface and is compressing a horizontal spring by $8 c m$ $8 cm$ . If the spring's constant is $2 \frac{k g}{s^{2}}$ $2 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2017-12-21T13:54:07

The coefficient of static friction is $= 0.0054$ $=0.0054$

The mass is $m = 3 k g$ $m=3kg$

The compression of the spring is $x = 0.08 m$ $x=0.08m$

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

The reaction of the spring is $R = k x = 2 \cdot 0.08 = 0.16 N$ $R=kx=2*0.08=0.16N$

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

The normal reaction of the object is $N = m g = 3 \cdot 9.8 = 29.4 N$ $N=mg=3*9.8=29.4N$

The coefficient of static friction is

$μ_{s} = \frac{R}{N} = \frac{0.16}{29.4} = 0.0054$ $mu_s=R/N=0.16/29.4=0.0054$

An object with a mass of 3kg 3 kg is lying on a surface and is compressing a horizontal spring by 8cm8 cm. If the spring's constant is 2kgs2 2 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?