An object with a mass of $15 k g$ $15 kg$ is lying on a surface and is compressing a horizontal spring by $10 c m$ $10 cm$ . If the spring's constant is $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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An object with a mass of $15 k g$ $15 kg$ is lying on a surface and is compressing a horizontal spring by $10 c m$ $10 cm$ . If the spring's constant is $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2017-02-17T16:58:36

The minimum coefficient of static friction is $μ = 5.4 \cdot 10^{- 3}$ $mu = 5.4 * 10^-3$ .

Explanation:

We know that the frictional force due to static friction will be the normal force of the object on the surface times the coefficient of static friction, $μ$ $mu$ . The normal force, in turn, is simply the block's mass times the force of gravity:

$F = - μ N$ $F = -mu N$
$F = - g m μ$ $F = -g m mu$

And Hooke's law tells us that the force due to the spring is...

$F = - k x$ $F = -kx$

These two values will be equal when $μ$ $mu$ is at the minimum to keep the block stationary, so we can set the equations equal and plug in given values.

$- k x = - g m μ$ $-kx = -g m mu$
$k x = g m μ$ $kx = g m mu$
$8 \cdot .1 = 9.8 \cdot 15 \cdot μ$ $8*.1 = 9.8*15*mu$
$.8 = 147 μ$ $.8 = 147mu$
$0.0054 = μ$ $0.0054 = mu$

And using scientific notation to simplify we get:

$μ = 5.4 \cdot 10^{- 3}$ $mu = 5.4 * 10^-3$

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An object with a mass of $15 k g$ $15 kg$ is lying on a surface and is compressing a horizontal spring by $10 c m$ $10 cm$ . If the spring's constant is $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

1 Answer

Explanation:

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An object with a mass of 15kg 15 kg is lying on a surface and is compressing a horizontal spring by 10cm10 cm. If the spring's constant is 8kgs2 8 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

1 Answer

Explanation:

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An object with a mass of $15 k g$ $15 kg$ is lying on a surface and is compressing a horizontal spring by $10 c m$ $10 cm$ . If the spring's constant is $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?