A 100-newton box is moving on a horizontal surface. A force of 10 newtons applied parallel to the surface is required to keep the box moving at constant velocity. What is the maximum coefficient of kinetic friction between the box and the surface?
To determine the maximum coefficient of kinetic friction between the box and the surface, we need to calculate the force of kinetic friction acting on the box.
The force required to keep the box moving at a constant velocity is equal to the force of kinetic friction:
\(F_{\text{{applied}}} = F_{\text{{kinetic friction}}}\)
\(10 \text{{ N}} = F_{\text{{kinetic friction}}}\)
Since the force of kinetic friction is given by:
\(F_{\text{{kinetic friction}}} = \mu_k \cdot N\)
where \(N\) is the normal force acting on the box and \(\mu_k\) is the coefficient of kinetic friction.
The normal force acting on the box is equal to the weight of the box:
\(N = mg = 100 \text{{ N}}\)
Therefore:
\(F_{\text{{kinetic friction}}} = \mu_k \cdot 100 \text{{ N}}\)
Since \(F_{\text{{kinetic friction}}} = 10 \text{{ N}}\), we can solve for \(\mu_k\) as follows:
\(10 \text{{ N}} = \mu_k \cdot 100 \text{{ N}}\)
\(\mu_k = \frac{10 \text{{ N}}}{100 \text{{ N}}} = 0.1\)
Therefore, the maximum coefficient of kinetic friction between the box and the surface is 0.1.