A 5.0- kg concrete block rests on a level table. A 3.7- kg mass is attached to the block by a string passing over a light, frictionless pulley. If the acceleration of the block is measured to be 1.0 m/s2, what is the coefficient of friction between the block and the table?

To find the coefficient of friction between the block and the table, we need to use Newton's second law of motion and the concept of friction.

First, let's start by calculating the net force acting on the system. Since the acceleration is measured, we can assume the mass of the system is the total mass of both the block and the attached mass.

1. Calculate the total mass of the system:
Total mass = mass of block + mass of attached mass
= 5.0 kg + 3.7 kg
= 8.7 kg

2. Calculate the net force acting on the system:
Net force = total mass × acceleration
= 8.7 kg × 1.0 m/s^2
= 8.7 N

According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force is equal to the force of gravity pulling the system down, which is countered by the force of friction acting in the opposite direction.

3. Calculate the force of gravity pulling the system down:
Force of gravity = mass of system × acceleration due to gravity
= 8.7 kg × 9.8 m/s^2
= 85.26 N

4. Calculate the force of friction using:
Force of friction = mass of block × acceleration + mass of attached mass × acceleration
= (5.0 kg + 3.7 kg) × 1.0 m/s^2
= 8.7 N

Now we have the force of friction and the force of gravity. The force of friction is equal in magnitude but opposite in direction to the force of gravity. So, we can write:

Force of friction = coefficient of friction × force of gravity

5. Rearrange the equation to solve for the coefficient of friction:
Coefficient of friction = Force of friction / Force of gravity
= 8.7 N / 85.26 N
≈ 0.102

Therefore, the coefficient of friction between the block and the table is approximately 0.102.