An object with a mass of # 3 kg# is lying still on a surface and is compressing a horizontal spring by #80 c m#. If the spring's constant is # 6 (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 still on a surface and is compressing a horizontal spring by #80  c   m#. If the spring's constant is # 6  (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Olivia Askew · Accepted Answer

The coefficient of static friction is #=0.16#

The mass is #m=3kg#

The compression of the spring is #x=0.80m#

The spring constant is #k=6kgs^-2#

The reaction of the spring is #R=kx=6*0.8=4.8N#

The acceleration due to gravity is #g=9.8ms^-2#

The normal reaction of the object is

#N=mg=3*9.8=29.4N#

The coefficient of static friction is

#mu_s=R/N=4.8/29.4=0.16#

Emily Abbate · Answer

undefined To find the minimum value of the coefficient of static friction, use the equation $ \mu_s = \frac{kx}{mg} + \frac{f}{mg} $, where:
- $ \mu_s $ is the coefficient of static friction,
- $ k $ is the spring constant (6 kg/s²),
- $ x $ is the compression of the spring (0.80 m),
- $ m $ is the mass of the object (3 kg),
- $ g $ is the acceleration due to gravity (9.8 m/s²),
- $ f $ is the force exerted by the spring ($ kx $).

Substitute the given values into the equation and solve for $ \mu_s $.