An object with a mass of $12 k g$ $12 kg$ is lying still on a surface and is compressing a horizontal spring by $\frac{1}{3} m$ $1/3 m$ . 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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An object with a mass of $12 k g$ $12 kg$ is lying still on a surface and is compressing a horizontal spring by $\frac{1}{3} m$ $1/3 m$ . 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 · 2016-04-23T05:30:21

Force F required to compress a spring by x unit is
$F = k \cdot x$ $F=k*x$ ,where k = force constant.
Here $x = \frac{1}{3} m$ $x =1/3m$
$k = 4 k g s^{- 2}$ $k=4kgs^-2$
hence Force exerted on the object of mass 1 kg is $F = 4 \frac{k g}{s^{2}} \times \frac{1}{3} m = \frac{4}{3} \frac{k g \cdot m}{s^{2}} = \frac{4}{3} N$ $F=4(kg)/s^2xx1/3m=4/3(kg*m)/s^2=4/3N$
This force is balanced by the then static frictional force as it is self adjusting one,

So the minimum value of the coefficient of static frictions
$μ_{s} = \frac{F}{N}$ $mu_s=F/N$ ,where N is the normal reaction exerted on the body by the floor. Here $N = m g = 12 \cdot 9.8 N$ $N =mg=12*9.8N$
So
$μ_{s} = \frac{F}{N} = \frac{\frac{4}{3}}{9.8 \times 12} = 0.011$ $mu_s=F/N=(4/3)/(9.8xx12)=0.011$

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An object with a mass of $12 k g$ $12 kg$ is lying still on a surface and is compressing a horizontal spring by $\frac{1}{3} m$ $1/3 m$ . 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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An object with a mass of 12kg12 kg is lying still on a surface and is compressing a horizontal spring by 13m1/3 m. If the spring's constant is 4kgs24 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

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An object with a mass of $12 k g$ $12 kg$ is lying still on a surface and is compressing a horizontal spring by $\frac{1}{3} m$ $1/3 m$ . 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?