Final answer:
The mass of block 2 can be calculated by using Newton's second law and the given acceleration and mass of block 1, considering that the system is frictionless and using the gravitational acceleration.
Step-by-step explanation:
Given that the mass of block 1 (m1) is 24 kg and the acceleration (a) of the system is 0.642 m/s² in the clockwise direction, to calculate the mass of block 2 (m2), we can use Newton's second law of motion. As per the problem statement, we are considering a scenario where there is no friction present in the system.
Since the system is accelerating in the clockwise direction, this implies that block 2 must be heavier than block 1 for it to pull block 1 upwards. To determine the mass of block 2, we can apply the following formula derived from Newton's second law:
F = m * a
where F is the net force on the system, m is the mass being accelerated, and a is the acceleration. In a frictionless pulley system with two blocks, the net force is the difference in weight (mass times gravitational acceleration) of the two blocks.
Therefore the net force (F) will be the weight of block 2 minus the weight of block 1:
F = m2 * g - m1 * g = (m2 - m1) * g
And since F is also equal to the total mass of the system times the acceleration, we get:
(m2 - m1) * g = (m1 + m2) * a
Now, by plugging in the values we know (m1, a, and using g = 9.81 m/s² for the acceleration due to gravity), we can solve for m2:
(m2 - 24 kg) * 9.81 m/s² = (24 kg + m2) * 0.642 m/s²
Expanding and rearranging the terms gives us a solvable equation for m2, which we can then solve to find the mass of block 2.