An object with a mass of #4 kg# is lying still on a surface and is compressing a horizontal spring by #1/4 m#. If the spring's constant is # 8 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Question

An object with a mass of #4     kg# is lying still on a surface and is compressing a horizontal spring by #1/4 m#. If the spring's constant is # 8 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Sebastian Acosta · Accepted Answer

The coefficient of static friction is #=0.051#

The static friction coefficient is

#mu_s=F_r/N#

#F_r=k*x#

The spring constant is #k=8kgs^-2#

The compression is #x=1/4m#

Consequently,

#F_r=8*1/4=2N#

The typical force is

#N=mg=4gN#

The static friction coefficient is

#F_r=2/(4g)=0.051#

Parker Abbott · Answer

undefined The minimum value of the surface's coefficient of static friction can be calculated using the formula: coefficient of static friction = (spring constant * compression distance) / (mass * gravity). Plugging in the given values: spring constant = 8 (kg)/s², compression distance = 1/4 m, mass = 4 kg, and gravity = 9.8 m/s², the calculation yields a minimum coefficient of static friction of approximately 0.51.