Introduction:
In this scenario, we have two masses, m1 and m2, on which a force of 5N is applied. We are given that the force produces an acceleration of 8m/s^2 in m1 and an acceleration of 24m/s^2 in m2. We need to determine the acceleration when both masses are tied together.

Given:
Force (F) = 5N
Acceleration of m1 (a1) = 8m/s^2
Acceleration of m2 (a2) = 24m/s^2

Using Newton's second law of motion:
The force acting on an object is equal to the mass of the object multiplied by its acceleration.
F = m * a

Calculating the mass of m1:
Using the given force and acceleration for m1, we can rearrange the equation to find the mass of m1.
m1 = F / a1
m1 = 5N / 8m/s^2
m1 = 0.625 kg

Calculating the mass of m2:
Using the given force and acceleration for m2, we can calculate the mass of m2 using the same equation.
m2 = F / a2
m2 = 5N / 24m/s^2
m2 = 0.208 kg

Calculating the total mass (m) when both masses are tied together:
When both masses are tied together, they move as a single object with a combined mass.
m = m1 + m2
m = 0.625 kg + 0.208 kg
m = 0.833 kg

Calculating the acceleration when both masses are tied together:
Now that we have the total mass, we can calculate the acceleration using the force applied.
F = m * a
a = F / m
a = 5N / 0.833 kg
a ≈ 6 m/s^2

Explanation:
When both masses are tied together, they experience the same force. The force applied to each mass is the same, regardless of their individual accelerations. However, since the masses have different masses, the force causes different accelerations in each mass. The mass with a smaller value will experience a larger acceleration.

When the masses are tied together, we calculate the total mass by adding the individual masses. The acceleration of the combined masses can be determined by dividing the applied force by the total mass. In this case, the acceleration of the combined masses is approximately 6 m/s^2.

Conclusion:
When both m1 and m2 are tied together, they experience an acceleration of approximately 6 m/s^2.