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, we can use the concept of centripetal force. In a circular motion, the centripetal force is provided by the horizontal component of the lift force.
The formula for centripetal force is:
Fc = (mv^2) / r
Where Fc is the centripetal force, m is the mass of the jet, v is the velocity, and r is the radius of the turn.
Plugging in the given values:
Fc = (2.40 × 10^5 kg) × (138 m/s)^2 / 3810 m
Fc = (2.40 × 10^5 kg) × (19044 m^2/s^2) / 3810 m
Fc = 11972080000 kg m^2/s^2 / 3810 m
Fc = 3142210.498 kg m/s^2
Therefore, the magnitude of the necessary lifting force is approximately 3,142,210.498 N.
To calculate the magnitude of the necessary lifting force, we first need to determine the centripetal force acting on the jet as it makes a horizontal circular turn. The centripetal force is provided by the horizontal component of the lifting force.
We can use the formula for centripetal force:
Fc = mv^2 / r
where Fc is the centripetal force, m is the mass of the jet, v is the velocity of the jet, and r is the radius of the circular turn.
Plugging in the given values:
Fc = (2.40 × 10^5 kg) × (138 m/s)^2 / (3810 m)
Calculating this expression will give us the magnitude of the centripetal force, which is equal to the magnitude of the necessary lifting force.