A jet (m = 4.00 105 kg), flying at 139 m/s, banks to make a horizontal circular turn. The radius of the turn is 3810 m. Calculate the necessary lifting force.
Regardless of the radius and velocity, the vertical component of the lift force must balance the weight, M g.
L cos A = M g
where L is the lift force. It is perpendicular to the wing, not straight up.
To get the vertical component, you must know the "banking angle", A. You can get this from
L sin A = M V^2/R (Tilting of the plane creates a horizontal lift component to provide the centripetal force)
To get L alone, square both equations and add
L = M*sqrt[g^2 + V^4/R^2]
To calculate the necessary lifting force, we need to consider the forces acting on the jet in the vertical direction.
The lifting force is provided by the vertical component of the net force on the jet. This net force is the centripetal force required to keep the jet moving in a circular path.
The centripetal force is given by the equation:
Fc = m * v^2 / r
Where:
- Fc is the centripetal force
- m is the mass of the jet
- v is the velocity of the jet
- r is the radius of the turn
Substituting the given values:
Fc = (4.00 * 10^5 kg) * (139 m/s)^2 / 3810 m
Simplifying the equation:
Fc = 401807.88 N
Therefore, the necessary lifting force is approximately 401807.88 Newtons.
To calculate the necessary lifting force for the jet, we need to consider the forces acting on it. In a horizontal circular turn, there are two main forces at play: the gravitational force (mg) and the centripetal force (Fc).
The gravitational force (mg) is given by:
mg = mass (m) * acceleration due to gravity (g)
In this case, the mass of the jet (m) is given as 4.00 * 10^5 kg.
The centripetal force (Fc) is given by:
Fc = mass (m) * radius (r) * angular velocity squared (ω^2)
In this case, the radius of the turn (r) is given as 3810 m, and the velocity (v) is given as 139 m/s. The angular velocity (ω) can be calculated using the formula:
ω = v / r
Now we can replace the ω in the above equation to get the centripetal force (Fc).
Finally, the lifting force (FL) is the vertical component of the net force acting on the jet. In this case, it is equal to the gravitational force (mg).
To summarize, the steps to calculate the necessary lifting force are as follows:
1. Calculate the gravitational force (mg) using the formula, mg = m * g.
2. Calculate the angular velocity (ω) using the formula, ω = v / r.
3. Calculate the centripetal force (Fc) using the formula, Fc = m * r * ω^2.
4. Calculate the lifting force (FL) which is equal to the gravitational force (mg).