A jet flying at 138 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is 2.40 × 105 kg. Calculate the magnitude of the necessary lifting force.
To calculate the magnitude of the necessary lifting force, you can use the centripetal force equation.
The centripetal force, Fc, is given by the formula:
Fc = (m * v^2) / r
where:
m is the mass of the jet (2.40 × 10^5 kg)
v is the velocity of the jet (138 m/s)
r is the radius of the turn (3810 m)
Plugging in the values, you can calculate the necessary lifting force:
Fc = (2.40 × 10^5 kg * (138 m/s)^2) / 3810 m
Calculating this, the centripetal force is:
Fc = (2.40 × 10^5 kg * 138^2 m^2/s^2) / 3810 m
Fc ≈ 2.87 × 10^7 N
Therefore, the magnitude of the necessary lifting force is approximately 2.87 × 10^7 N.