An object with a mass of $12 k g$ $12 kg$ is lying on a surface and is compressing a horizontal spring by $50 c m$ $50 cm$ . If the spring's constant is $6 \frac{k g}{s^{2}}$ $6 (kg)/s^2$ , 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 on a surface and is compressing a horizontal spring by $50 c m$ $50 cm$ . If the spring's constant is $6 \frac{k g}{s^{2}}$ $6 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2016-07-13T06:17:18

$μ_{s} \geq 0.025$ $mu_s>=0.025$

Explanation:

The situation here is that the spring is already compressed by $0.5 m$ $0.5m$ and the object is at rest as the surface is with friction.

That means force of friction and spring force are balancing each other out.

$F_{s} = F_{f}$ $F_s=F_f$

Spring forces is $F_{s} = k x$ $F_s=kx$ Given $k = 6 k \frac{g}{s^{2}}$ $k=6kg/s^2$ and $x = 0.5 m$ $x=0.5m$
$F_{s} = 6 \cdot 0.5 = 3 N$ $F_s=6*0.5=3N$

Now, frictional force depends on the normal force of the body. Since the surface is horizontal, the entire weight of the body is the normal force. So, $F_{f} = μ_{s} \cdot N = μ_{s} \cdot m \cdot g = μ_{s} \cdot 12 \cdot 10$ $F_f=\mu_s*N=\mu_s*m*g=\mu_s*12*10$

Equating the two, $cancel3^1=\mu_s*cancel120^40$

So, that's how the minimum static constant is so small.

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An object with a mass of $12 k g$ $12 kg$ is lying on a surface and is compressing a horizontal spring by $50 c m$ $50 cm$ . If the spring's constant is $6 \frac{k g}{s^{2}}$ $6 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Explanation:

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An object with a mass of 12 kg12kg 12 kg is lying on a surface and is compressing a horizontal spring by 50 cm50cm50 cm. If the spring's constant is 6 (kg)/s^26kgs2 6 (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 on a surface and is compressing a horizontal spring by $50 c m$ $50 cm$ . If the spring's constant is $6 \frac{k g}{s^{2}}$ $6 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?