A jet flying at 135 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is 1.82*10^5 kg.
Calculate the magnitude of the necessary lifting force.
thanks for the detailed explanation
The sarcasm is real
Well, if a jet wants to make a circular turn, it needs a lifting force to counteract the gravitational force and keep it from nosediving into the ground. Let's calculate it in a funny way:
To find the necessary lifting force, we need to consider the centrifugal force and the weight of the jet. It's like trying to balance a plate of spaghetti on a stick while riding a unicycle, except in this case, the plate is the lifting force, and the unicycle is the jet (wait, do jets ride unicycles?).
First, let's find the centrifugal force acting on the jet. It's given by the equation:
F_cent = m * v^2 / r
Where:
m = mass of the jet = 1.82 * 10^5 kg
v = velocity of the jet = 135 m/s
r = radius of the turn = 3810 m
Now, substituting the values into the equation:
F_cent = (1.82 * 10^5 kg) * (135 m/s)^2 / 3810 m
Calculating this circus act gives us the centrifugal force.
And the answer is... (drumroll please)...
F_cent = 3.2447316 * 10^6 N
But wait, we're not done yet! We still need to add the weight of the jet to find the total lifting force.
So, the lifting force is like summoning the strength of Hercules to carry the jet against gravity. It's given by:
F_lift = F_cent + m * g
Where:
m = mass of the jet = 1.82 * 10^5 kg
g = acceleration due to gravity = 9.8 m/s^2 (Gravity, always pulling us down!)
Now, substituting the values into the equation:
F_lift = 3.2447316 * 10^6 N + (1.82 * 10^5 kg) * (9.8 m/s^2)
After carefully balancing this equation, we find the magnitude of the necessary lifting force.
And voila! The magnitude of the necessary lifting force is... (ta-da!)...
F_lift = 3.540924 * 10^6 N
So, the jet needs a lifting force of approximately 3.540924 * 10^6 Newtons to make that circular turn. That's a lot of lifting power! I hope it doesn't skip arm day at the gym.
To calculate the magnitude of the necessary lifting force, we can start by using the centripetal force equation:
F_c = (m * v^2) / r
Where:
F_c is the centripetal force
m is the mass of the jet
v is the velocity of the jet
r is the radius of the circular turn
Plugging in the given values:
m = 1.82 * 10^5 kg
v = 135 m/s
r = 3810 m
F_c = (1.82 * 10^5 kg * (135 m/s)^2) / 3810 m
Now we can simplify this equation and calculate the result.
The necessary force must include a vertical component (mg), and a horizontal component (mv^2/r)
then magnitude is sqrt(vertical^2+horizontal^2)