Final answer:
To get the block to barely begin moving on a surface with friction, a force equal to the maximum static friction must be applied. This maximum static friction is calculated using the coefficient of static friction and the normal force. Upon exceeding this force, the block will move at constant velocity if kinetic friction is counterbalanced by the applied force.
Step-by-step explanation:
When considering a pulley system with friction, we analyze the forces at the moment when a block begins to move. Initially, the block is stationary due to static friction, which must be overcome by an applied force to initiate motion. Once this threshold force, also known as the maximum static friction force, is exceeded, the block will start to move, and kinetic friction takes over. Kinetic friction, although usually less than static friction, continually opposes the block's motion.
To calculate the force required to just move the blocks, the following steps are followed:
- Determine the force due to gravity acting on the coupled blocks, which is the weight (m·g).
- Calculate the maximum static friction using the coefficient of static friction (μ) and the normal force, which is the weight of the block for a horizontal surface.
- Resolve all forces acting on each block including the tension in the rope and the friction.
- Set up the equations of motion, considering that the system initially remains at rest until the applied force equals the maximum static friction force.
- Solve these equations, finding the applied force necessary to get the blocks moving.
Once motion begins, the static friction transitions to kinetic friction, which, provided that the applied force remains constant, results in a constant velocity of the blocks due to Newton's first law of motion.