An object with a mass of $3$ $3$ $k g$ $kg$ is lying on a surface and is compressing a horizontal spring by $10$ $10$ $c m$ $cm$ . If the spring's constant is $9$ $9$ $k g s^{- 2}$ $kgs^-2$ , what is the minimum value of the surface's coefficient of static friction?

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An object with a mass of $3$ $3$ $k g$ $kg$ is lying on a surface and is compressing a horizontal spring by $10$ $10$ $c m$ $cm$ . If the spring's constant is $9$ $9$ $k g s^{- 2}$ $kgs^-2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2016-04-07T21:46:19

The frictional coefficient $μ = 0.03$ $mu=0.03$ .

Explanation:

(convert the distance to SI units: $10$ $10$ $c m$ $cm$ = $0.1$ $0.1$ $m$ $m$ )

The force exerted by the spring is given by:

$F = k x = 9 \times 0.1 = 0.9$ $F=kx=9xx0.1=0.9$ $N$ $N$

Since the object is stationary, this force applied by the spring must be being balanced by the frictional force.

The frictional force is given by:

$F_{frict} = μ F_{normal}$ $F_"frict"=muF_"normal"$

And the normal force is the gravitational force:

$F_{normal} = m g = 3 \times 9.8 = 29.4$ $F_"normal"=mg=3xx9.8=29.4$ $N$ $N$

Rearranging:

$μ = \frac{F_{frict}}{F_{normal}} = \frac{0.9}{29.4} = 0.03$ $mu=F_"frict"/F_"normal"=0.9/29.4=0.03$

(frictional coefficients do not have units)

(side note: I keep saying that $k g s^{- 2}$ $kgs^-2$ is an odd unit for spring constant. It is correct, but so is $N m^{- 1}$ $Nm^-1$ , and the latter makes is easier to understand what is going on in most contexts.)

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An object with a mass of $3$ $3$ $k g$ $kg$ is lying on a surface and is compressing a horizontal spring by $10$ $10$ $c m$ $cm$ . If the spring's constant is $9$ $9$ $k g s^{- 2}$ $kgs^-2$ , 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 3 3 kgkg is lying on a surface and is compressing a horizontal spring by 1010 cmcm. If the spring's constant is 9 9 kgs−2kgs^-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 $3$ $3$ $k g$ $kg$ is lying on a surface and is compressing a horizontal spring by $10$ $10$ $c m$ $cm$ . If the spring's constant is $9$ $9$ $k g s^{- 2}$ $kgs^-2$ , what is the minimum value of the surface's coefficient of static friction?