Question

A 2200-kg
airplane pulls two gliders, the first of mass 350 kg
and the second of mass 250 kg
, down the runway with an acceleration of 1.3 m/s2
(Figure 1). Neglect the mass of the two ropes and any frictional forces. Determine the magnitude of the tension force in the second rope.

Answers

GPT-4o mini
To determine the tension force in the second rope, we can use Newton's second law of motion, \(F = ma\).

### Step 1: Calculate the total mass being pulled.

The total mass consists of the airplane and both gliders:

\[
m_{\text{total}} = m_{\text{airplane}} + m_{\text{glider 1}} + m_{\text{glider 2}} = 2200\, \text{kg} + 350\, \text{kg} + 250\, \text{kg} = 2800\, \text{kg}
\]

### Step 2: Calculate the total force acting on the system.

Using Newton's second law, we can find the total force required to accelerate this mass:

\[
F_{\text{total}} = m_{\text{total}} \cdot a = 2800\, \text{kg} \cdot 1.3\, \text{m/s}^2 = 3640\, \text{N}
\]

### Step 3: Consider the forces on the second glider.

Now, we examine the forces acting on the second glider (the glider with mass \(250\, \text{kg}\)). The total force acting on it can be expressed as:

\[
F_{\text{tension}} - F_{\text{glider}} = m_{\text{glider}} \cdot a
\]

Where:
- \(F_{\text{tension}}\) is the tension in the second rope (which we need to find),
- \(F_{\text{glider}} = m_{\text{glider}} \cdot g\) only applies if we are considering weight in a vertical direction, and since we neglect friction and are in horizontal linear motion, we skip that consideration here.

### Step 4: Apply Newton's second law to the second glider.

Substituting our values for the second glider \(F_{\text{tension}} - 0 = m_{\text{glider}} \cdot a\):

\[
F_{\text{tension}} = m_{\text{glider}} \cdot a
\]

Where:
- \( m_{\text{glider}} = 250\, \text{kg} \)
- \( a = 1.3\, \text{m/s}^2 \)

### Step 5: Calculate the tension force.

\[
F_{\text{tension}} = 250\, \text{kg} \cdot 1.3\, \text{m/s}^2 = 325\, \text{N}
\]

### Conclusion

The magnitude of the tension force in the second rope is:

\[
\boxed{325\, \text{N}}
\]