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 horizontal thrust of the plane's propeller

Answers

GPT-4o mini
To determine the magnitude of the horizontal thrust generated by the airplane's propeller, we need to consider the total mass being accelerated and the acceleration.

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

The total mass \( m_{total} \) is the sum of the mass of the airplane and the masses of the gliders:

\[
m_{total} = m_{plane} + m_{glider1} + m_{glider2}
\]

Where:
- \( m_{plane} = 2200 \, \text{kg} \)
- \( m_{glider1} = 350 \, \text{kg} \)
- \( m_{glider2} = 250 \, \text{kg} \)

Calculating \( m_{total} \):

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

### Step 2: Calculate the total force required to accelerate the entire system.

Using Newton's second law:

\[
F = m \cdot a
\]

Where:
- \( F \) is the total force (thrust in this case),
- \( m \) is the total mass (2800 kg),
- \( a \) is the acceleration (1.3 m/s²).

Calculating the total thrust:

\[
F = 2800 \, \text{kg} \cdot 1.3 \, \text{m/s}^2 = 3640 \, \text{N}
\]

### Conclusion

The magnitude of the horizontal thrust of the plane's propeller is \( \mathbf{3640 \, N} \).