Final answer:
To determine the static coefficient of friction on the table's surface, analyze the forces at the point where the hanging block's weight is about to move the block on the table. Calculate the force of static friction by equating it to the gravitational force component (along the string) of the hanging block.
Step-by-step explanation:
The student has asked what is the static coefficient of friction between a block on a table's surface and the surface itself, given the block's mass and the set-up where additional weight will cause the block to move. To find the static coefficient of friction (μ_s), we analyze the forces acting on both blocks in the system. The tension in the horizontal and the inclined string will be the same at the threshold of movement since the strings are under continuous tension without any acceleration. We can calculate the static friction force (μ_s × normal force) exerted by the block on the table which is equal to the component of gravitational force pulling the hanging block (mass × gravity × sin(θ)).
As soon as the hanging block's weight exceeds the static friction force, the block on the table will start to slide. This situation represents the maximum static friction force that equals the weight of the hanging block just at the point of sliding. Thus, μ_s = (hanging mass × g) / (table mass × g) where g is the acceleration due to gravity, and we consider the component of the weight acting along the incline due to the string's angle. Knowing the masses and g, we can solve for the static coefficient of friction μ_s.