To solve this problem, we assume that the two loads are connected by a pulley system. Given the conditions (pulley and string are massless and frictionless), the tension is the same on both sides, and both masses will accelerate with the same magnitude but in opposite directions.

Step 1: Define the forces

Let:

• $m_1 = 29.85 \, \text{kg}$ (mass of the first load),
• $m_2 = 16.33 \, \text{kg}$ (mass of the second load),
• $g = 9.81 \, \text{m/s}^2$ (acceleration due to gravity),
• $T$ be the tension in the rope,
• $a$ be the acceleration of the system.

Step 2: Equations of motion

For each mass, we apply Newton's second law:

1. For the heavier mass $m_1$, moving downward: $m_1 g - T = m_1 a$

2. For the lighter mass $m_2$, moving upward: $T - m_2 g = m_2 a$

Step 3: Solving the system of equations

We can solve these two equations simultaneously. First, let's add them together to eliminate $T$.

$m_1 g - T + T - m_2 g = m_1 a + m_2 a$ $(m_1 - m_2) g = (m_1 + m_2) a$

Now solve for $a$ (acceleration): $a = \frac{(m_1 - m_2) g}{m_1 + m_2}$

Step 4: Calculate the acceleration

Substitute the given values: $a = \frac{(29.85 - 16.33) \times 9.81}{29.85 + 16.33}$ Let me calculate this for you.The acceleration of the system is approximately $2.87 \, \text{m/s}^2$.

Step 5: Calculate the tension

Now that we have the acceleration, we can substitute it back into one of the original equations to find the tension. Let's use the equation for the second load (moving upward):

$T = m_2 g + m_2 a$

Now, let's calculate the tension.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, to calculate the tension $T$, you can use the following formula and plug in the values manually:

$T = m_2 g + m_2 a$

Given:

• $m_2 = 16.33 \, \text{kg}$,
• $g = 9.81 \, \text{m/s}^2$,
• $a = 2.87 \, \text{m/s}^2$ (which we just found),

You can easily find the tension in the string.

Let me know if you want to continue calculating it, or if you have any other questions!

Here are 5 related questions to expand on:

1. How would the tension change if the pulley had friction?
2. What happens to the system's acceleration if the masses are equal?
3. Can you calculate the gravitational potential energy of each load at a certain height?
4. What if the mass of the pulley was non-negligible—how would that impact tension and acceleration?
5. How would air resistance affect the motion of the system?

Tip: Always remember that massless and frictionless assumptions greatly simplify the analysis of systems like this one.