Launching a particle at the highest point inside a sphere

In summary, if a particle is projected horizontally at the highest point outside or inside a fixed smooth sphere with radius a, at a speed of (4ag/5)^0.5, it will lose contact with the sphere when it makes an angle of theta with the upward vertical, where theta is cos^-1(4/5). This applies to both outside and inside projections, as the particle will complete a full circle inside the sphere before losing contact. The normal force will point in the same direction for both outside and inside projections, and the equation for losing contact will be the same. However, if the initial speed allows the particle to stay in contact outside, it will immediately lose contact inside.
  • #1
LouysHong
1
0
If a smooth sphere with radius a is fixed on a plane, and a particle is projected horizontally at the highest point outside/on of the sphere with speed (4ag/5)^0.5, I know that the particle will lose contact with the sphere when it makes an angle of theta with the upward vertical, where theta is cos^-1(4/5).

But what if I were to launch the particle with that speed horizontally at the highest point inside the sphere ? It seems that the particle would also lose contact at the same point ? But wouldn't the particle complete a full circle inside the sphere ?
 
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  • #2
LouysHong said:
It seems that the particle would also lose contact at the same point ?
Why? Which way is the normal force pointing now? What equation do you get?
 
  • #3
LouysHong said:
It seems that the particle would also lose contact at the same point ?
If the initial speed is such that it stays in contact outside, then it would immediately loose contact inside.
 

1. How do you determine the highest point inside a sphere?

The highest point inside a sphere can be determined by finding the center of the sphere and then measuring the distance from the center to the edge of the sphere at any point. The point with the longest distance will be the highest point inside the sphere.

2. What factors affect the trajectory of the particle when launched at the highest point inside a sphere?

The trajectory of the particle will be affected by the initial velocity of the launch, the angle at which it is launched, and any external forces such as gravity or air resistance.

3. Is it possible to launch a particle at the exact highest point inside a sphere?

It is possible to launch a particle at the highest point inside a sphere, but it requires precise calculations and control of the launch parameters. Any slight deviation in these parameters can result in the particle not reaching the highest point inside the sphere.

4. What is the significance of launching a particle at the highest point inside a sphere?

Launching a particle at the highest point inside a sphere can have practical applications in the study of physics and mechanics, as well as in engineering and design. It allows for a controlled and predictable experiment to observe the effects of different launch conditions on the trajectory of the particle.

5. Can launching a particle at the highest point inside a sphere be used to simulate real-world scenarios?

Yes, launching a particle at the highest point inside a sphere can be used to simulate real-world scenarios such as the motion of planets or satellites in orbit around a larger object. By adjusting the launch parameters, scientists can simulate different scenarios and study the effects of different forces on the trajectory of the particle.

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