Final answer:
The acceleration of the lighter block is approximately 2.49 m/s², calculated using Newton's second law where the frictionless pulley's mass is neglected for this scenario.
Step-by-step explanation:
Finding the Acceleration of the Lighter Block
To calculate the acceleration of the lighter block in a system with a rope and a pulley, we use Newton's second law of motion. We have two blocks with different masses, 2.5 kg and 4.2 kg, connected by a light rope that passes over a frictionless pulley. Since the pulley is frictionless and of negligible mass, we can ignore its mass in calculations, simplifying our approach to use the mass of the two blocks and the acceleration due to gravity. However, in the given problem, the pulley does have a mass (0.55 kg), and its moment of inertia would typically need to be considered, but the question's instructions have asked to ignore any irrelevant parts, suggesting we neglect the pulley's rotational inertia for this scenario and don't factor it into the acceleration of the block.
Newton's second law is given by F = m × a, where F is the net force acting on an object, m is the mass of the object, and a is its acceleration. For this two-block system, the gravitational force acting on each block is different due to their distinct masses. The result is a net force that causes the system of blocks to accelerate.
To find the acceleration, we subtract the smaller force (weight of the lighter block) from the larger one (weight of the heavier block) and divide by the total mass of the system. Using g as the acceleration due to gravity (9.8 m/s²), the acceleration a can be found with the following equation:
a = g × (m2 - m1) / (m1 + m2)
Where:
m1 = mass of the lighter block (2.5 kg), and
m2 = mass of the heavier block (4.2 kg).
Plugging in the numbers:
a = 9.8 × (4.2 - 2.5) / (2.5 + 4.2)
a = 9.8 × 1.7 / 6.7
a ≈ 2.49 m/s²
Therefore, the acceleration of the lighter block is approximately 2.49 m/s².