Final answer:
The acceleration of the two-block system, one block on a frictionless table and another hanging vertically, with masses 1.5 kg and 2 kg respectively, is approximately 5.29 m/s².
Step-by-step explanation:
To calculate the acceleration of the system with masses m₁ = 1.5 kg and m₂ = 2 kg, we can use Newton's second law of motion.
Since the table is frictionless and we are neglecting the mass of the pulley, the only forces doing work on the system are the weight of the hanging mass and the tension in the string.
However, the tension acts on both masses in opposite directions and thus does not affect the overall acceleration of the system.
Therefore, we only consider the unbalanced force due to gravity on the hanging mass.
Let's define the downward direction as positive for the hanging mass. The force due to gravity on the hanging mass is F = m₂*g, and since there is no friction, this force will be the net force causing the acceleration of the entire system.
Applying Newton's second law F = (m₁ + m₂)*a, where F is the net force and a is the acceleration, we get:
m₂*g = (m₁ + m₂)*a
a = m₂*g / (m₁ + m₂)
Substituting the given values, we find:
a = 2*9.8 / (1.5 + 2)
a ≈ 5.29 m/s²
This is the acceleration of the entire system.
Question: A block of mass m₁ = 1.5 kg is placed on a frictionless table. It is connected by a string that passes over a pulley to a second block of mass m₂ = 2 kg hanging vertically. The system is released from rest. Given that the acceleration due to gravity is 9.8m/s², calculate the acceleration of the system.