A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.87x103 m. During this performance the pilot whose weight is 821 N, maintains a constant speed of 2.10x102 m/s. (a) When the pilot is at the highest point of the loop determine his apparent weight. N (b) At what speed will the pilot experience weightlessness? m/s (c) When the pilot is at the lowest point of the loop determine his apparent weight. N
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.
A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.87x103 m. During this performance the pilot whose weight is 821 N, maintains a constant speed of 2.10x102 m/s.
(a) When the pilot is at the highest point of the loop determine his apparent weight.
N
(b) At what speed will the pilot experience weightlessness?
m/s
(c) When the pilot is at the lowest point of the loop determine his apparent weight.
N
![### Circular Motion and Centripetal Force
In the study of circular motion, understanding the relationship between velocity, radius, and centripetal force is crucial. The diagram provided can help illustrate these concepts.
#### Diagram Explanation:
- **Object in Circular Motion:** The diagram depicts an object moving in a circular path.
- **Path of Motion:** The dashed circle represents the trajectory of the object.
- **Velocity Vectors (→v and →v'):**
- Two arrows pointing tangentially to the circle (one to the right and one to the left) represent the tangential velocities (→v and →v') of the object at two different points along the path.
- The direction of these velocity vectors shows that the object is moving along the circular path at a constant speed but continuously changing direction.
- **Radius (R):**
- A line segment (denoted as R) extends from the center of the circle to the object's position on the path.
- This represents the radius of the circular path and is perpendicular to the velocity vector at any given point.
- **Direction of Motion:** The object moves in a counter-clockwise direction around the circle, as indicated by the positioning and orientation of the velocity vectors.
#### Centripetal Force:
- The object in circular motion experiences a centripetal force directed towards the center of the circle. This force is responsible for continuously changing the direction of the velocity vector, keeping the object on its circular path.
- While not explicitly shown in the diagram, understanding that this inward force (centripetal force) is essential to maintain circular motion is important.
In summary, this diagram effectively illustrates the fundamental principles of circular motion, highlighting the relationships between the radius, tangential velocity, and the continuous change in direction experienced by an object in uniform circular motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81610fbc-71d4-4f51-a970-c974c7e9c894%2F287bdc4d-df21-4664-9a55-17d6fde06788%2Fpbt9s7a_processed.jpeg&w=3840&q=75)
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