The system below is in equilibrium, but it begins to slip
ifany additional mass is added to the 5.0 kg object. what is
thecoefficient of static friction between the 10 kg block and
theplane on which it rests?

The coefficient of static friction between the 10kg block and the surface is 0.29. Which was calculated by applying newtons first law of motion as it applies to equilibrium situations.

Explanation:

The steps for the solution to this problem can be found in the attachment below. The first thing to do in problems like this is to draw free body diagrams that clearly shows the forces acting of the elements of the system. Next, you apply newtons law(s) of motion as the case may be and then solve for your unknowns. It is easier to resolve the forces acting at a point into their horizontal and vertical components. This makes the solution to the problem easier.

For this solution, the sign convention used assumed towards as positive, downwards as negative, the right as positive and the left as negative. Best wishes.

b. a lightning bug, plug of grass, and a worm