An object with a mass of $8 kg$ is lying still on a surface and is compressing a horizontal spring by $5/4 m$ . If the spring's constant is $3 (kg)/s^2$ , what is the minimum value of the surface's coefficient of static friction?

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Answer 1 · 2016-12-20T00:44:08

The static coefficient must equal 0.048

We are looking at a case of balanced forces here. The force of the spring $F=kx$ will push on the mass with a force of

$F = (3(kg)/s^2)(5/4m)$ = $15/4$ N

Static friction will be equal in magnitude to this, as there is no motion.

Writing the force of friction as $F_f=muF_N = mumg$

$15/4N = mu (8kg)(9.8m/s^2)$

$3.75 N = muxx78.4N$

$mu=3.75/78.4 = 0.048$

An object with a mass of 8 kg8 kg is lying still on a surface and is compressing a horizontal spring by 5/4 m5/4 m. If the spring's constant is 3 (kg)/s^23 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?