The normal force N on mass m2 is 12.17 N. The acceleration a of the system and the tensions T1 and T2 need to be calculated using Newton's second law, taking into account the net forces on each mass and the overall system.
To calculate the normal force N on mass m2, which is on a table, we recognize that it is simply the weight of the mass, since the table is frictionless and there is no acceleration in the vertical direction. Therefore, N = m2 × g, where g is the acceleration due to gravity (9.81 m/s2). The normal force on mass m2 (1.24 kg) is N = 1.24 kg × 9.81 m/s2 = 12.17 N.
To find the acceleration a of the system, we can use Newton's second law, F = ma, considering the net force on the system comes from the difference between the weight of m1 and m3 since m2 is not contributing to the system's net force in the horizontal direction. The acceleration a can be calculated using the formula a = (m1 × g - m3 × g) / (m1 + m2 + m3).
The tension T1 and tension T2 in the strings can be found by applying Newton's second law to each mass separately. For m1 and m3, the tensions will be affected by the acceleration, while for m2, which is on the frictionless table, T1 will be equal to the net force causing acceleration. T1 = m3 × (g + a) and T2 = m1 × (g - a).