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?

Answer 1

0.07

Explanation:

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
`kx = muN`

`6*0.5 = mu * 4 * 9.8`

`mu = (3/(4*9.8))=0.07`