A jet airplane is in level flight. The mass of the airplane is m = 8870 kg. The plane travels at a constant speed around a circular path of radius R = 9.55 miles and makes one revolution every T = 0.126 hours. What is the magnitude of the lift force acting on the plane?

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Because it wanted to experience some "air"-raising acrobatics!

To calculate the magnitude of the lift force acting on the plane, we need to consider the centripetal force required to keep the airplane in circular motion. The centripetal force is provided by the lift force.

The magnitude of the lift force (F) can be calculated using the equation:

F = (m * v^2) / r

where m is the mass of the airplane, v is the velocity of the plane, and r is the radius of the circular path.

First, let's convert the given values to SI units:
- Mass (m) = 8870 kg
- Radius (r) = 9.55 miles = 15.361 km

To find the velocity (v), we need to convert the time it takes to make one revolution (T) to seconds:
- Time (T) = 0.126 hours = 0.126 * 3600 seconds = 453.6 seconds

Now, we can calculate the velocity (v):
- Velocity (v) = 2πr / T

Substituting the values into the equation, we have:
- Velocity (v) = 2π * 15.361 / 453.6

Now, plug in the values to calculate the magnitude of the lift force:
- F = (8870 * v^2) / r

And voila! You've got the magnitude of the lift force acting on the plane. Remember, though, this calculation assumes idealized conditions and doesn't account for other factors like air resistance and turbulence. So, take it with a grain of laughter! Keep the skies safe and amusing!

To find the magnitude of the lift force acting on the plane, we can start by calculating the net force acting on the plane.

The net force acting on the airplane in level flight can be calculated using the centripetal force formula:

F_net = m * (v^2 / R)

Where:
- F_net is the net force acting on the plane
- m is the mass of the airplane
- v is the velocity of the airplane
- R is the radius of the circular path

We can calculate the velocity of the airplane by dividing the circumference of the circular path by the time it takes to complete one revolution:

v = (2πR) / T

So, substituting this into the formula, we get:

F_net = m * (((2πR) / T)^2 / R)

Now let's calculate the magnitude of the lift force by subtracting the weight of the airplane from the net force. The weight can be calculated using the formula:

weight = m * g

Where:
- weight is the weight force acting on the plane
- g is the acceleration due to gravity

Finally, the magnitude of the lift force (L) can be found by subtracting the weight from the net force:

L = F_net - weight

Now let's substitute the given values into the formulas and calculate the magnitude of the lift force.

To find the magnitude of the lift force acting on the plane, we can use the following equation:

Lift force = (mass * velocity^2) / radius

First, we need to find the velocity of the plane. The formula for velocity is:

velocity = 2π * radius / time

Given the radius R = 9.55 miles and the time T = 0.126 hours, we can calculate the velocity:

velocity = 2π * 9.55 miles / 0.126 hours

To perform this calculation, we need to convert the units to be consistent. Let's convert miles to meters and hours to seconds:

1 mile = 1.60934 km = 1609.34 m
1 hour = 60 minutes = 60 * 60 seconds = 3600 seconds

Substituting these values into the velocity equation:

velocity = 2π * (9.55 miles * 1609.34 m/mile) / (0.126 hours * 3600 s/hour)

Simplifying the equation:

velocity = 2π * (9.55 * 1609.34) / (0.126 * 3600) m/s

Now, let's calculate the velocity.

velocity = 2π * (9.55 * 1609.34) / (0.126 * 3600) m/s

Once we have the velocity, we can substitute it along with the mass (m = 8870 kg) and radius (R = 9.55 miles) into the lift force equation:

Lift force = (mass * velocity^2) / radius

Plugging in the values:

Lift force = (8870 kg * velocity^2) / (9.55 miles * 1609.34 m/mile)

Finally, calculate the magnitude of the lift force.

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