An object with a mass of # 4 kg# is lying on a surface and is compressing a horizontal spring by #50 cm#. 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 #  4 kg# is lying on a surface and is compressing a horizontal spring by #50   cm#. If the spring's constant is #  6  (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Sebastian Acosta · Accepted Answer

0.07 <img src="https://tutor.hix.ai First, the coefficient of static friction increases with force. At the current moment, lets say the coeff is u . 
So the horizontal force of friction is u*N where N is the normal reaction force equal to the weight of the body.
So, N = M*g where g is acceleration due to gravity.
Now, let's calculate the force exerted by the spring. We know it is -k*x where k is the spring constant and x is the displacement.
If the body is not moving, we can equate the forces.
hence 
<mathjax>#kx = muN #
<mathjax># 6*0.5 = mu * 4 * 9.8 #
<mathjax>#mu = (3/(4*9.8))=0.07#

Benjamin Asiedu · Answer

undefined The minimum value of the surface's coefficient of static friction is 0.3.