To find the magnitude of the acceleration of the blocks, we need to use Newton's second law and consider the net force on each block individually. However, with the given information, we find that there is no solution to this problem. Please double-check the problem statement or provide more information.
To find the magnitude of the acceleration of the blocks, we need to use Newton's second law, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, both blocks are connected by a rope and pulley system, so they will have the same acceleration. The net force on each block can be determined by considering the forces acting on each block individually.
Let's assume that Block 1 has a mass of m₁ and Block 2 has a mass of m₂. According to the given information, m₁ = 1.5 * m₂. The force due to gravity on each block can be determined using F = m * g, where m is the mass and g is the acceleration due to gravity.
The net force on Block 1 (F₁_net) is equal to the force due to gravity on Block 1 minus the tension in the rope (T). The net force on Block 2 (F₂_net) is equal to the force due to gravity on Block 2 plus the tension in the rope (T). Since the blocks have the same acceleration, we can set up the following equations:
F₁_net = m₁ * g - T
F₂_net = m₂ * g + T
Since m₁ = 1.5 * m₂, we can substitute this value into the equations:
F₁_net = 1.5 * m₂ * g - T
F₂_net = m₂ * g + T
Next, we can set up an equation for the net force on the system, which is equal to the mass of the system (m₁ + m₂) times the acceleration (a):
F_net = (1.5 * m₂ + m₂) * g = (2.5 * m₂) * g
Since the net force is equal to the sum of the individual net forces:
F_net = F₁_net + F₂_net
Substituting the previously derived equations:
(2.5 * m₂) * g = 1.5 * m₂ * g - T + m₂ * g + T
Simplifying the equation:
(2.5 * m₂) * g = 1.5 * m₂ * g + m₂ * g
Dividing both sides of the equation by (2.5 * m₂ * g):
1 = 1.5 + 1
1 = 2.5
Since this equation is not true, we have reached a contradiction. Therefore, there is no solution to this problem using the given information. Please check the problem statement again or provide more information if necessary.