What is the speed and normal force of a bead sliding around a loop-the-loop?

In summary, the conversation discusses a problem involving a bead sliding without friction around a loop-the-loop. It is released from a height of 3.30R and the goal is to find its speed at point A and the normal force on it at that point. The solution involves treating the loop as a falling object and using equations for potential and kinetic energy to find the speed. To find the normal force, a force diagram is used and the equation F=ma is applied. The final answer for the normal force is 0.06899 N.
  • #1
Sheneron
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0

Homework Statement


A bead slides without friction around a loop-the-loop (Fig. P8.5). The bead is released from a height h = 3.30R.

http://img530.imageshack.us/my.php?image=p815ye0.gif

(a) What is its speed at point A? Answer in terms of R and g, the acceleration of gravity.
(b) How large is the normal force on it at this point if its mass is 4.40 g?

The Attempt at a Solution


Having some trouble with both parts. Thanks.
 
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  • #2
Think of this problem as a falling loop, there is no friction, so just treat the loop as if it has rolled down and had its center of mass accelerated at 9.8m/s^2 down a wall height h. now simply use the equations for potential and kinetic energy and you're done.
 
  • #3
Alright I think I got A.

mgy=1/2 mv^2 so g(3.3-2)=1/2v^2

so that leaves, v= (g2.6R)^.5

But still need help with B
 
  • #4
Draw a force diagram at point A. The forces acting on the particle are mg (down) and normal force (down). The acceleration is v^2/r. F=ma.
 
  • #5
Excellent, I found the answer.

Fn = ma - mg

Fn = m(2.6gR)/R - mg
Fn = .0044(2.6*9.8) - .0044(9.8) = .06899 N

Thanks for the help
 

1. What is the meaning of "Conservation of Energy" in relation to beads?

The conservation of energy refers to the principle that energy cannot be created or destroyed, but only transferred or transformed. In the case of beads, this means that the total amount of energy within a system of beads will remain constant, even if the beads are moving or interacting with each other.

2. How does the conservation of energy apply to the movement of beads?

When beads are in motion, the conservation of energy means that the total amount of kinetic energy (energy of motion) and potential energy (stored energy) will remain constant. This means that as one bead gains kinetic energy by moving, another bead in the system will lose an equal amount of kinetic energy. The same principle applies to potential energy, such as when a bead is lifted to a higher position.

3. Can the conservation of energy be violated with beads?

No, the conservation of energy is a fundamental law of physics and cannot be violated. This means that in any system of beads, the total amount of energy will always remain constant, even if the beads are moving or interacting with each other.

4. How is the conservation of energy related to the concept of energy transfer in beads?

In the context of beads, energy transfer refers to the transfer of energy from one bead to another, or between a bead and its surroundings. The conservation of energy means that during this transfer, the total amount of energy in the system will remain constant. For example, when a bead hits another bead and transfers some of its kinetic energy, the total amount of kinetic energy in the system will remain the same.

5. What are some practical applications of the conservation of energy in relation to beads?

The conservation of energy has many practical applications in the world of beads. For example, it can be used to analyze the motion of beads in a necklace or bracelet, or to understand the energy transfer involved in a bead-making process. It can also be used to design efficient bead sorting machines or to optimize the energy usage in bead manufacturing processes.

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