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

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Answer 1 · 2016-07-04T11:24:53

The force exerted by the spring is $F = k x = 3 \times \frac{1}{4} = \frac{3}{4}$ $F=kx=3xx1/4=3/4$ $N$ $N$ .

The frictional force is given by $F_{frict} = μ F_{norm} = μ m g = μ \times 1 \times 9.8$ $F_"frict"=muF_"norm"=mumg=muxx1xx9.8$ $N$ $N$

The frictional force must be at least equal to the spring force, so:

$9.8 μ = \frac{3}{4}$ $9.8mu=3/4$ , and rearranging, $μ = 0.076$ $mu=0.076$ (no units).

An object with a mass of 11 kgkg is lying still on a surface and is compressing a horizontal spring by 141/4 mm. If the spring's constant is 33 kgs−2kgs^-2, what is the minimum value of the surface's coefficient of static friction?