A jet flying at 132 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is 1.68 × 105 kg. Calculate the magnitude of the necessary lifting force.
Instead of thinking up new names to post with, try working the problems. Help will be provided to those who show work.
To calculate the magnitude of the necessary lifting force, we need to consider the forces acting on the jet in this situation.
In a horizontal circular turn, there are two main forces involved: the gravitational force (weight) acting vertically downward and the lifting force (centripetal force) acting perpendicular to the wings of the jet.
Let's break down the steps to find the magnitude of the necessary lifting force:
Step 1: Calculate the gravitational force acting on the jet.
The gravitational force, also known as weight (W), can be calculated using the formula:
W = mass × acceleration due to gravity (g)
Given the mass of the jet: 1.68 × 10^5 kg
Acceleration due to gravity: 9.8 m/s^2
W = 1.68 × 10^5 kg × 9.8 m/s^2
Step 2: Calculate the centripetal force (lifting force).
In a horizontal circular turn, the centripetal force is responsible for keeping the jet moving in a curved path. The centripetal force is given by the formula:
Centripetal force (F) = mass × velocity^2 ÷ radius
Given:
Velocity (v) = 132 m/s
Radius (r) = 3810 m
F = 1.68 × 10^5 kg × (132 m/s)^2 ÷ 3810 m
Step 3: Find the magnitude of the lifting force.
The lifting force (F) is the centripetal force required for the jet to maintain its circular path. So, the magnitude of the necessary lifting force is equal to the centripetal force.
F = [1.68 × 10^5 kg × (132 m/s)^2] ÷ 3810 m
Now, you can calculate the magnitude of the necessary lifting force using the given values in the formula.
If you plug in the values into the formula and calculate, you will find the answer for the magnitude of the necessary lifting force.