An object with a mass of # 3 kg# is lying on a surface and is compressing a horizontal spring by #20 cm#. If the spring's constant is # 9 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Question

An object with a mass of #  3   kg# is lying on a surface and is compressing a horizontal spring by #20 cm#. If the spring's constant is #  9  (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Elena Albarran · Accepted Answer

The minimum value of the coefficient of static friction is 0.06.

It is my understanding that you are requesting the lowest coefficient of static friction on the surface at which the spring will not be able to move the mass. The spring exerts a horizontal force of #F_"spring" = k * Deltax = 9 "kg"/s^2 * 0.2 m = 1.8" kg"*m/s^2 = 1.8 N# Friction needs to be able to oppose that force with an equal and opposite force to maintain its grip. The force of friction is #F_f = mu_s*N# where N is the component if the object's weight normal to the surface. I assume the surface is horizontal, so N is the object's full weight. #F_f = mu_s*m*g # #1.8 N = mu_s*3 kg*(9.8 m)/s^2 = mu_s*(29.4 kg*m)/s^2 = mu_s*29.4 N# Solving for #mu_s#, #mu_s = (1.8 cancel(N))/(29.4 cancel(N)) = 0.06# Hope this is helpful, Steve.

Julia Aguilar · Answer

undefined The minimum value of the surface's coefficient of static friction can be calculated using the formula:

Coefficient of static friction (μ) = (spring constant × compression distance) / (mass × acceleration due to gravity)

Substituting the given values:

μ = (9 (kg/s^2) × 0.20 m) / (3 kg × 9.8 m/s^2)
μ ≈ 0.0612

So, the minimum value of the surface's coefficient of static friction is approximately 0.0612.