The net external force on the propeller of a 3.9 kg model airplane is 7.2 N forward. What is the acceleration of the airplane?
The Correct Answer and Explanation is :
To solve this problem, we can apply Newton’s Second Law of Motion, which states:
[
F = ma
]
Where:
- ( F ) is the net external force acting on the object (in this case, the airplane’s propeller),
- ( m ) is the mass of the object (the airplane), and
- ( a ) is the acceleration of the object.
Given:
- The mass of the airplane, ( m = 3.9 \, \text{kg} ),
- The net external force on the propeller, ( F = 7.2 \, \text{N} ).
Step 1: Rearranging the formula to solve for acceleration (( a )):
[
a = \frac{F}{m}
]
Step 2: Plugging in the known values:
[
a = \frac{7.2 \, \text{N}}{3.9 \, \text{kg}}
]
Step 3: Performing the calculation:
[
a = 1.846 \, \text{m/s}^2
]
Answer:
The acceleration of the airplane is approximately 1.85 m/s².
Explanation:
Newton’s Second Law tells us that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, the propeller applies a forward force of 7.2 N on the airplane. The mass of the airplane is given as 3.9 kg. By dividing the force by the mass, we determine the acceleration. The unit of force (Newton, N) is equivalent to kg·m/s², and this ensures that the resulting acceleration is in units of m/s².
The positive value of the acceleration indicates that the airplane is speeding up in the direction of the applied force, which is forward. If there were any resistive forces, like air resistance, they would need to be accounted for as part of the net force to adjust the acceleration accordingly. In this case, we are given that 7.2 N is the net external force, so we assume other forces, if present, have already been factored in.