A jet flying at 120 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is 2.19 × 105 kg. Calculate the magnitude of the necessary lifting force.
L =____ N
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To calculate the magnitude of the necessary lifting force, we can use the principle of circular motion, which states that the net force acting on an object moving in a circle must be directed toward the center of the circle. In this case, the lifting force provides the necessary centripetal force to keep the jet in the circular turn.
The centripetal force (F_c) required for an object moving in a circular path can be calculated using the formula:
F_c = (m * v^2) / r
where:
F_c = centripetal force
m = mass of the object
v = velocity of the object
r = radius of the circular path
In this case, the mass of the jet is given as 2.19 × 10^5 kg, the velocity is 120 m/s, and the radius of the circular path is 3810 m.
Substituting these values into the formula, we get:
F_c = (2.19 × 10^5 kg) * (120 m/s)^2 / 3810 m
Calculating this expression, we find:
F_c ≈ 1.45 × 10^6 N
Therefore, the magnitude of the necessary lifting force is approximately 1.45 × 10^6 N.