Velocity Equal Along Curved Paths?

In summary, if two bodies are falling vertically and along a curved surface, with corresponding points at the same height from the surface of the earth and a parallel line connecting them, neglecting friction, the velocity acquired at the two points will be equal. This can be proven using energy considerations, as both bodies will have lost the same amount of potential energy at the same vertical height. This also implies that their kinetic energy will be equal. However, this only applies if the curved surface is smooth and the object makes contact with it at only one point.
  • #1
batballbat
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Lets say a body is falling vertically . Another body is falling along a curved surface maybe like a combination of helix and inclined plane. taking any two corresponding points of the paths, such that the points are at same height from the surface of earth. Or in other words the line joining the points is parallel to horizontal surface. Will the velocity acquired at the two points be equal. Prove it.

Ps. The acceleration of the body in such a curved path won't be uniform. Also neglect friction
 
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  • #2
If you neglect friction (both air and with the curved surface) then you can apply energy considerations. At the same vertical height both bodies will have lost the same amount of potential energy.
What does this tell you about their kinetic energy?

(I'm assuming the curved surface you refer to is smooth and the object makes contact with it at only one point)
 

1. What is the concept of velocity equal along curved paths?

The concept of velocity equal along curved paths is a principle in physics that states that the velocity of an object remains constant along a curved path if the force acting on the object is perpendicular to its velocity. This means that the object is not accelerating, and its direction of motion is changing at a constant rate.

2. How is velocity equal along curved paths different from velocity on a straight path?

Velocity equal along curved paths is different from velocity on a straight path because on a curved path, the direction of motion is constantly changing, while on a straight path, the object continues to move in the same direction at a constant speed. This means that the object on a curved path is experiencing acceleration due to a change in direction, while an object on a straight path is not.

3. Can velocity be equal along all types of curved paths?

Yes, velocity can be equal along all types of curved paths as long as the force acting on the object is perpendicular to its velocity. This holds true for any type of curved path, including circles, ellipses, and parabolas.

4. How does the concept of velocity equal along curved paths relate to the laws of motion?

The concept of velocity equal along curved paths is a result of the first law of motion, also known as the law of inertia. This law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. In the case of a curved path, the external force acts perpendicular to the object's velocity, causing it to change direction but not speed.

5. What are some real-life applications of velocity equal along curved paths?

Velocity equal along curved paths has many real-life applications, including the motion of objects in orbit, the movement of cars around a banked curve, and the flight of a basketball through the air. It also plays a role in designing roller coasters and other amusement park rides.

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