Final answer:
The magnitude of the force necessary to move two sliding blocks at constant speed is equal to the frictional force, which is calculated by multiplying the coefficient of kinetic friction by the product of the gravitational force and the mass of the blocks.
Step-by-step explanation:
To find the magnitude of the force necessary to move the blocks at a constant speed, we must consider the effects of kinetic friction. Since we are dealing with a kinetic friction coefficient of 0.400, and the system involves two blocks sliding against each other, the kinetic frictional force is the product of this coefficient, the normal force, and the mass of the blocks.
To keep the blocks moving at a constant speed, the applied force must overcome the frictional force. The frictional force (Ffriction) can be calculated using the equation Ffriction = μk × N, where μk is the coefficient of kinetic friction and N is the normal force, which is equal to the gravitational force for a horizontal surface. Thus, Ffriction = 0.400 × (4.00 kg × 9.8 m/s²).
Once we have the frictional force, the necessary force to move the blocks at constant speed is simply an equal and opposite force to the frictional force. This is because a net force of zero is required for a constant speed, based on Newton's first law of motion. Therefore, the magnitude of the force necessary is equal to the calculated frictional force.