During an episode of turbulence in an airplane you feel 180 N heavier than usual.
Part A
If your mass is 86 kg, what are the magnitude and direction of the airplane’s acceleration?
F = ma
To determine the magnitude and direction of the airplane's acceleration, we need to make use of Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration.
Step 1: Calculate the force exerted on you due to your weight.
The force due to gravity on an object is given by the equation F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth). In this case, since you feel 180 N heavier than usual, the net force acting on you would be F = mg + 180 N.
F = (86 kg)(9.8 m/s²) + 180 N
Step 2: Calculate the net force acting on you in terms of acceleration.
According to Newton's second law, we can write the equation as F = ma, where a is the acceleration of the airplane.
ma = (86 kg)(9.8 m/s²) + 180 N
Simplifying the equation:
86a = (86 kg)(9.8 m/s²) + 180 N
Step 3: Solve for the acceleration.
Divide both sides of the equation by 86 kg to isolate the acceleration:
a = [(86 kg)(9.8 m/s²) + 180 N] / 86 kg
Now perform the calculations:
a ≈ [(84.28 kg · m/s²) + 180 N] / 86 kg
a ≈ 10.06 m/s²
The magnitude of the airplane's acceleration is approximately 10.06 m/s².
Step 4: Determine the direction of the acceleration.
Since you feel 180 N heavier, we can conclude that the direction of the acceleration is downward, opposite to the upward force that counteracts your weight.
Therefore, the direction of the airplane's acceleration is downward.