Introduction:
In this scenario, we have two masses, m1 and m2, that are acted upon by a force of 5N. We are given that the force causes m1 to accelerate at 8m/s^2 and m2 to accelerate at 24m/s^2. We need to determine the acceleration when both masses are tied together.

Analysis:
To understand the concept of acceleration when masses are tied together, we need to consider Newton's second law of motion. According to this law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, this can be represented as:

F = ma

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

Calculating the acceleration of m1:
Given that the force acting on m1 is 5N and the acceleration of m1 is 8m/s^2, we can rearrange the formula to solve for m1:

F = m1 * a1
5 = m1 * 8
m1 = 5/8

Calculating the acceleration of m2:
Similarly, given that the force acting on m2 is 5N and the acceleration of m2 is 24m/s^2, we can solve for m2:

F = m2 * a2
5 = m2 * 24
m2 = 5/24

Calculating the acceleration when both masses are tied together:
When both masses are tied together, they experience the same force. Thus, the net force acting on both masses is still 5N. Let's assume the combined mass of m1 and m2 is M. Then we can write:

F = M * a_combined

Since the net force is the same, we can equate the expressions for F:

m1 * a1 = M * a_combined
(5/8) * 8 = M * a_combined
5 = M * a_combined

Similarly, for m2:

m2 * a2 = M * a_combined
(5/24) * 24 = M * a_combined
5 = M * a_combined

From both equations, we can see that the acceleration when both masses are tied together is the same as the individual accelerations of m1 and m2, which is 5m/s^2.

Conclusion:
When both masses are tied together and subjected to a force of 5N, the acceleration they experience is 5m/s^2. This means that the combined mass of m1 and m2 does not affect the acceleration in this scenario.