Final answer:
The acceleration of the system composed of two blocks with masses m₁ = 1.0 kg and m₂ = 0.57 kg, with a horizontal force of 0.5 N applied to m₁, is approximately 0.3185 m/s² by applying Newton's second law.
Step-by-step explanation:
The subject of the problem is Physics, and it essentially involves Newton's second law of motion, which states that the force applied to an object equals the mass of the object multiplied by its acceleration (F = ma). To calculate the magnitude of the acceleration of the system comprising two blocks, we must consider the total mass of the system and the net force applied.
Since there is only one external horizontal force acting on m₁, and assuming there are no other forces (like friction) acting on the system, the same force F is responsible for the acceleration of both m1 and m2 together.
To find the acceleration, we use the formula:
a = F / (m₁ + m₂)
Substituting the given values:
a = 0.5 N / (1.0 kg + 0.57 kg)
The calculated acceleration is approximately:
a = 0.5 N / 1.57 kg = 0.3185 m/s²
Therefore, the acceleration of the system is approximately 0.3185 m/s².