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
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 \( \mathbf{3640 \, N} \).
### 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 \( \mathbf{3640 \, N} \).