The magnitude of the force that the blocks exert on each other is 2.5 N for block A and 1.5 N for block B.
Step-by-step explanation:
To find the magnitude of the force that the blocks exert on each other, we can use Newton's second law of motion. According to this law, the net force on an object is equal to its mass multiplied by its acceleration. In this case, the blocks are connected and move together, so their acceleration is the same.
First, we need to find the acceleration of the system of blocks. We can use the formula: net force = mass × acceleration. The applied force of 4.0 N is the net force on the system because there is no friction or other external forces mentioned.
So, net force = 4.0 N, mass = 10 kg + 6.0 kg = 16.0 kg. Rearranging the formula, we get: acceleration = net force / mass = 4.0 N / 16.0 kg = 0.25 m/s².
Since both blocks have the same acceleration, the force exerted on each block is equal. We can find the magnitude of this force using the formula: force = mass × acceleration. For block A with a mass of 10 kg, the force = 10 kg × 0.25 m/s² = 2.5 N. For block B with a mass of 6.0 kg, the force = 6.0 kg × 0.25 m/s² = 1.5 N.