A boy is sat at a semisphere with a ray of 18.4 m. He starts sliding. On what height will the boy loose contact with the sphere? There is no friction.
1 Answer
12.3 m
Explanation:
Key concepts needed for the solution:
- Centripetal force as a net force
- Conservation of energy
r = radius of the sphere
When the boy is sliding down the hemisphere, he experiences a centripetal force:
There are two forces contribute the centripetal (net) force, the normal force and gravitation pull. Note that the boy's motion at any instant on the sphere is tangential to the hemispheric arc. It can be shown by geometry that the force pushing radially on to the sphere due to the boy's weight is
At the moment the boy loss contact with the sphere, N=0.
Friction free means that we can apply conservation of energy to this scenario. And together with the equation above, we get: