## Question

###### 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?

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?

## Answers

The static coefficient must equal 0.048

## Explanation:

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# NStatic 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#

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