An object with a mass of $8 k g$ $8 kg$ 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 $3 \frac{k g}{s^{2}}$ $3 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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An object with a mass of $8 k g$ $8 kg$ 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 $3 \frac{k g}{s^{2}}$ $3 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2018-02-04T17:40:26

If the object compresses the spring by $\frac{5}{6} m$ $5/6 m$ ,then the restoring force which acts on the particle to throw it away fr om the spring,to come back to its original length,must be balanced by frictional force.

So,this force is $F = 3 \times (\frac{5}{6}) N = \frac{5}{2} N$ $F= 3×(5/6) N = 5/2 N$ (using, $F = K x$ $F=Kx$ ,where, $K$ $K$ is the spring constant and $x$ $x$ is the amount of compression)

Now,frictional force acting is $μ \times N = μ m g$ $mu×N=mumg$ (where, $μ$ $mu$ is the coefficient of kinetic frictional force, and $μ$ $mu$ should be such that it can supply force upto $\frac{5}{2} N$ $5/2 N$ )

So,equating both,

$\frac{5}{2} = μ \times 8 \times 10$ $5/2 = mu×8×10$

Or, $μ = 0.03125$ $mu=0.03125$

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An object with a mass of $8 k g$ $8 kg$ 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 $3 \frac{k g}{s^{2}}$ $3 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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An object with a mass of $8 k g$ $8 kg$ 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 $3 \frac{k g}{s^{2}}$ $3 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?