Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in the figures below, where m1 = 10 kg and m2 = 19 kg. A force of 46 N is applied to the 19 kg box.

(a1) Determine the acceleration of the boxes

To determine the acceleration of the boxes, we can apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for Newton's second law is:

F = m * a

Where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, we have two boxes connected by a light string. The force is applied to the 19 kg box, and both boxes will experience the same acceleration since they are connected.

Let's calculate the acceleration:

Step 1: Determine the net force on the system
The net force on the system is equal to the force applied to the 19 kg box. In this case, the force is 46 N.

Step 2: Determine the total mass of the system
The total mass of the system is the sum of the masses of both boxes. m1 = 10 kg and m2 = 19 kg. So, the total mass, m, is 10 kg + 19 kg = 29 kg.

Step 3: Calculate the acceleration
Now we can plug the values into the formula F = m * a and solve for a:

46 N = 29 kg * a

Divide both sides by 29 kg:

a = 46 N / 29 kg

a ≈ 1.59 m/s²

So, the acceleration of the boxes is approximately 1.59 m/s².