An object with a mass of $3 k g$ $3 kg$ is lying still on a surface and is compressing a horizontal spring by $80 c m$ $80 c m$ . 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 · 2018-06-25T05:59:18

The coefficient of static friction is $= 0.109$ $=0.109$

The mass of the object is $m = 3 k g$ $m=3kg$

The compression of the spring is $x = 0.80 m$ $x=0.80m$

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

The reaction of the spring is $R = k x = 4 \cdot 0.8 = 3.2 N$ $R=kx=4*0.8=3.2N$

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

$μ_{s} = \frac{R}{N} = \frac{3.2}{29.4} = 0.109$ $mu_s=R/N=3.2/29.4=0.109$

An object with a mass of 3 kg3kg 3 kg is lying still on a surface and is compressing a horizontal spring by 80 c m80cm80 c m. If the spring's constant is 4 (kg)/s^24kgs2 4 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?