To find the tensions on t1 and t2, we need to consider the forces acting on each block separately and apply Newton's second law of motion (F = ma), where F is the net force, m is the mass, and a is the acceleration.
For Block 1: The only force acting on Block 1 is the tension t1. The net force on Block 1 is given by F1 = m1 * a, where m1 is the mass of Block 1 and a is the acceleration. Substituting the given values, we have F1 = 2 kg * 5 m/s^2 = 10 N.
Since the only force acting on Block 1 is t1, the tension t1 is equal to the net force F1. Therefore, t1 = 10 N.
For Block 2: The force acting on Block 2 is the tension t2 and the force due to the weight of Block 2. The weight of Block 2 is given by Fw = m2 * g, where m2 is the mass of Block 2 and g is the acceleration due to gravity (approximately 9.8 m/s^2). Substituting the given values, we have Fw = 5 kg * 9.8 m/s^2 = 49 N.
The net force on Block 2 is given by F2 = m2 * a, where m2 is the mass of Block 2 and a is the acceleration. Since Block 2 is accelerating at the same rate as Block 1 (5 m/s^2), the net force F2 is also equal to m2 * a. Substituting the given values, we have F2 = 5 kg * 5 m/s^2 = 25 N.
Since the net force F2 is the sum of the forces t2 and Fw, we can write the equation as F2 = t2 + Fw. Substituting the values, we have 25 N = t2 + 49 N. Rearranging the equation, we find t2 = 25 N - 49 N = -24 N.
Therefore, the tension on t1 is 10 N, and the tension on t2 is -24 N. The negative sign indicates that the tension t2 is acting in the opposite direction (to the left) compared to the applied force t1 (to the right).