A jet flying at 106 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.
Would I use the equation Fc=mv^2 / r ??
The horizontal component of the lift L is the centripetal force that holds
the plane in the circle.
L•sinφ = m•v²/R.
The vertical component of the lift supports the weight of the plane; therefore,
L•cosφ = m•g.
Dividing the first equation by the second gives
L•sinφ/ L•cosφ = tanφ =
= m•v²/ m•g •R =v²/ g •R =
= 106²/9.8•3810 =0.3
φ=16.75º.
L = m•g/cosφ =
= 2.4•10^5•9.8/cos16.75º=2.46•10^6 N
Oh, I love it when we talk about flying jets! But let me tell you, it's all about the lift, because without it, they would just be really expensive paperweights.
Now, to answer your question, yes, you're on the right track with the equation Fc = mv^2 / r. But remember, in this case, we're looking for the lifting force, not the centripetal force.
To calculate the magnitude of the necessary lifting force, you need to subtract the gravitational force from the net force. The gravitational force can be found using the formula Fg = mg, where m is the mass of the jet and g is the acceleration due to gravity.
Once you have the gravitational force, subtract it from the net force (Fc = mv^2 / r) to get the lifting force.
So, let's put it all together in a funny equation:
Flift = Fc - Fg
= (mv^2 / r) - mg
Just plug in the values for m, v, r, and g, and you'll have your answer. Happy flying (with math)!
Yes, you can use the equation Fc = mv^2 / r to calculate the magnitude of the necessary lifting force. This equation represents the centripetal force required for an object to move in a circular path with radius r and speed v.
Step 1: Identify the given values.
- Velocity of the jet (v) = 106 m/s
- Radius of the turn (r) = 3810 m
- Mass of the jet (m) = 2.40 × 10^5 kg
Step 2: Substitute the values into the equation.
Fc = (m * v^2) / r
Step 3: Calculate the magnitude of the lifting force.
- Fc = (2.40 × 10^5 kg) * (106 m/s)^2 / 3810 m
Performing the calculations:
Fc = (2.40 × 10^5) * (11236) / 3810
Fc = 704636 / 3810
Fc ≈ 184.75 kg·m/s^2 or Newton (N)
Therefore, the magnitude of the necessary lifting force is approximately 184.75 N.
Yes, you are correct. To determine the magnitude of the necessary lifting force, you can use the equation 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 turn.
In this case, the given values are:
- Velocity of the jet (v) = 106 m/s
- Radius of the turn (r) = 3810 m
- Mass of the jet (m) = 2.40 × 10^5 kg
To find the centripetal force, you need to substitute these values in the equation:
Fc = (m * v^2) / r
Plugging in the given values, the equation becomes:
Fc = (2.40 × 10^5 kg * (106 m/s)^2) / 3810 m
Calculating this expression will give you the magnitude of the necessary lifting force.