What is the Maximum Height for Sliding Off a Semi-Circle?

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In summary, the conversation discusses a problem involving a boy sliding down a semi-circle shaped igloo and finding the height at which he slides off. Various equations and approaches are suggested, including conservation of energy and considering forces acting on the boy. It is eventually revealed that the force acting on the boy which will be zero when he slides off is the centripetal force, leading to the solution.
  • #1
Noobcake
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Homework Statement


A boy sits on top of an igloo shaped like a semi-circle of Radius R. He begins to slide down the semi-circle. At what height above the ground does the boy slide off the semi-circle? Assume g=9.8 m/s2, and no friction.
http://img207.imageshack.us/img207/4010/probmd1.jpg [Broken]

Homework Equations


Conservation of energy? Or centrifugal force?

The Attempt at a Solution


Couldn't think of any starting points; tried conservation of energy, but failed. Answer is obviously in terms of R. Can anyone shed the light on this problem?
 
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  • #2
At each point you will need to consider how quickly the boy is moving around the exterior of the circle, and how much force on the boy directed towards the inside of the circle will be needed to keep him moving in a circle at that speed.
 
  • #3
I do not quite understand how I should break gravity into different vectors, or is it even the right approach finding the velocity? The force you are talking about is the centrifugal force right?
But, my teachers seems to be hinting that conservation of energy is needed. Care to explain further?
 
  • #4
Noobcake said:
I do not quite understand how I should break gravity into different vectors, or is it even the right approach finding the velocity? The force you are talking about is the centrifugal force right?
But, my teachers seems to be hinting that conservation of energy is needed. Care to explain further?

Conservation of energy will tell you the speed of the boy at any height. The speed is related to the centripetal force required to stay in circular motion. Consider all of the forces acting on the boy and resolve them into components in the direction of motion (tangent to the circle until he separates from it) and perpendicular to the motion (the radial direction).
 
  • #5
To give you a BIG hint:
WHICH force acting on the boy will be zero when he slides off the semi-circle?
 

1. What is the concept of "Sliding Off A Semi-Circle"?

"Sliding Off A Semi-Circle" refers to the behavior of an object as it slides off the edge of a semi-circular surface, such as a ramp or track.

2. What factors affect the sliding behavior off a semi-circle?

The sliding behavior off a semi-circle is affected by the weight, shape, and surface texture of the object, as well as the angle and curvature of the semi-circular surface.

3. How does friction play a role in the sliding off a semi-circle?

Friction is an important factor in the sliding off a semi-circle, as it determines the amount of resistance and control an object has while sliding on the surface. More friction will slow down the object, while less friction will allow it to slide faster.

4. Can the sliding behavior off a semi-circle be predicted?

Yes, the sliding behavior off a semi-circle can be predicted using mathematical equations that take into account the various factors mentioned above, such as weight, shape, surface texture, and friction.

5. How is the concept of "Sliding Off A Semi-Circle" applicable in real life?

The concept of "Sliding Off A Semi-Circle" has many real-life applications, such as in the design of roller coasters, ski slopes, and playground slides. It is also relevant in sports like skateboarding, skiing, and snowboarding, where understanding the sliding behavior off a curved surface is crucial for performance and safety.

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