To determine the force on m2 and the acceleration of m1, we can apply Newton's second law of motion to each block individually.
For m2: The force acting on m2 is given by Newton's second law as F2 = m2 * a2, where m2 is the mass of m2 and a2 is its acceleration. Plugging in the given values, we have: F2 = 3.8 kg * 2.6 m/s^2 F2 = 9.88 N
Therefore, the force acting on m2 is 9.88 N.
For m1: Since m1 and m2 are connected by a light spring, they experience an equal and opposite force from the spring. Therefore, the force on m1 is also 9.88 N in the opposite direction.
Now, let's find the acceleration of m1. We'll use the principle of conservation of momentum, assuming that the spring has negligible mass:
The force on m1 is given by F1 = m1 * a1, where F1 is the force acting on m1 and a1 is its acceleration. Since the force on m1 is provided by the spring force, which is equal in magnitude but opposite in direction to the force on m2, we have F1 = -F2.
Therefore, -F2 = m1 * a1.
Plugging in the values, we get: -9.88 N = 4.6 kg * a1
Solving for a1: a1 = -9.88 N / 4.6 kg a1 ≈ -2.15 m/s^2
Therefore, the acceleration of m1 is approximately -2.15 m/s^2 (negative sign indicates acceleration in the opposite direction to m2).