A jet flying at 130 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is 1.86 × 105 kg. Calculate the magnitude of the necessary lifting force. L -
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![### Calculating the Necessary Lifting Force for a Jet in Horizontal Circular Motion
**Problem Statement:**
A jet flying at 130 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is \(1.86 \times 10^5\) kg. Calculate the magnitude of the necessary lifting force.
**Given Data:**
- Velocity of the jet, \(v = 130 \, \text{m/s}\)
- Radius of the turn, \(r = 3810 \, \text{m}\)
- Mass of the jet, \(m = 1.86 \times 10^5 \, \text{kg}\)
**Objective:**
Find the magnitude of the lifting force, \(L\).
**Formula to Use:**
The necessary lifting force for an aircraft in horizontal circular turn can be calculated using the centripetal force formula:
\[ F_c = \frac{mv^2}{r} \]
Since the lifting force provides the centripetal force for horizontal circular motion:
\[ L = \frac{mv^2}{r} \]
Here,
- \(m\) is the mass of the object,
- \(v\) is the velocity,
- \(r\) is the radius of the circular path.
### Solution:
1. **Calculate the Centripetal Force:**
\[
F_c = \frac{mv^2}{r}
\]
2. **Substitute the Given Values:**
\[
F_c = \frac{(1.86 \times 10^5 \, \text{kg}) \times (130 \, \text{m/s})^2}{3810 \, \text{m}}
\]
3. **Perform the Calculation:**
\[
F_c = \frac{(1.86 \times 10^5) \times (16900)}{3810}
\]
\[
F_c = \frac{3.1434 \times 10^9}{3810}
\]
\[
F_c = 8.2544 \times 10^5 \, \text{N}
\]
Therefore, the magnitude of the necessary lifting force \(L\) for the jet is \(\boxed{825440 \, \text{N}}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30341bd5-9df6-4a1f-8fda-916b6928e177%2Fd4d8d09a-6d81-42ef-beb4-ac490210ab50%2Fmp0q7sn_processed.jpeg&w=3840&q=75)
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