Mechanics- Conservation of energy

In summary: If the pendulum consists of a bob on a rigid rod, it could even be under compression. But from the given answer it appears it is on a string. For that case, your assumption is correct, but it seems you did not actually write that equation. Pity.
  • #1
AlonZ
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Homework Statement
Need to find the angle from which a pendulum with the length L that reaches its lowest point will complete a full circle around a pivot which distance is from the lowest point is l
Relevant Equations
assume Tension at the highest point of the loop is 0, because that's the minimun for a full loop.
My, supposedly rational thought is that if the pendulum will drop from a height higher than the top of the loop's height, by the law of conservation of energy, it'll have enough velocity to complete the loop.
The teacher's final result shows a different approach.
Am I right? Wrong? Thanks
 

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  • #2
AlonZ said:
Homework Statement:: Need to find the angle from which a pendulum with the length L that reaches its lowest point will complete a full circle around a pivot which distance is from the lowest point is l
Relevant Equations:: assume Tension at the highest point of the loop is 0, because that's the minimun for a full loop.

My, supposedly rational thought is that if the pendulum will drop from a height higher than the top of the loop's height, by the law of conservation of energy, it'll have enough velocity to complete the loop.
The teacher's final result shows a different approach.
Am I right? Wrong? Thanks

What about the kinetic energy needed by the pendulum to complete the loop? If the pendulum has no KE at the top of the loop, it will fall straight down.
 
  • #3
that's why I say mgL(1-cos(a) ) > mg2l, once it's larger there is still some energy left as kinetic for the pendulum not to fall
 
  • #4
AlonZ said:
that's why I say mgL(1-cos(a) ) > mg2l, once it's larger there is still some energy left as kinetic for the pendulum not to fall
What's ##\cos(a)##?
 
  • #5
the expression for the height of the pendulum before the drop, you can see at the SS I sent
 
  • #6
AlonZ said:
the expression for the height of the pendulum before the drop, you can see at the SS I sent
Can you explain the question? How could a pendulum ever complete a loop?
 
  • #7
yes, as you can see, the red circle is a new pivot for the pendulum. once the rope hits the red pivot, it spins around it and with enough velocity, completes a loop. the question is what should be the minimum angle from which I'd have to drop the pendulum for it to complete that loop.
 

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  • #8
AlonZ said:
yes, as you can see, the red circle is a new pivot for the pendulum. once the rope hits the red pivot, it spins around it and with enough velocity, completing a loop. the question is what should be the minimum angle from which I'd have to drop the pendulum for it to complete that loop.

I'll repeat my first answer: you need kinetic energy at the top of the smaller loop. What you have calculated is the energy to reach the top of the loop, stop and fall straight down. You need the energy to complete a loop.
 
  • #9
I see your point, my thought was that if the pendulum reaches the small loop's highest point and still has the tiniest amount of energy it'll not fall.
Still a bit hard for me to understand why that is wrong.
 
  • #10
AlonZ said:
I see your point, my thought was that if the pendulum reaches the small loop's highest point and still has the tiniest amount of energy it'll not fall.
Still a bit hard for me to understand why that is wrong.
If it has a tiny amount of energy, it will fall in a very steep parabola, which is nearly a straight vertical line.

In order to complete the loop, the natural parabola of the motion must be outside the circle of the loop at the top. Which means the pendulum bob must have at least the KE for circular motion with ##g## as the centripetal force.

If it has less KE than this it will naturally fall inside the circle. If it has more KE it try to escape the circle, but be held in the circular trajectory by the tension in the string.
 
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  • #11
AlonZ said:
assume Tension at the highest point of the loop is 0, because that's the minimun for a full loop.
If the pendulum consists of a bob on a rigid rod, it could even be under compression. But from the given answer it appears it is on a string. For that case, your assumption is correct, but it seems you did not actually write that equation. Pity.
 
  • #12
alright think I'm getting the idea.. Thx for the help
 

FAQ: Mechanics- Conservation of energy

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.

2. What is the difference between potential and kinetic energy?

Potential energy is the energy an object has due to its position or state, while kinetic energy is the energy an object has due to its motion. Potential energy can be converted to kinetic energy and vice versa.

3. How is mechanical energy conserved in a system?

In a closed system, mechanical energy (the sum of potential and kinetic energy) remains constant. This means that as potential energy decreases, kinetic energy increases and vice versa, but the total amount of energy remains the same.

4. Can energy be lost in a mechanical system?

No, according to the law of conservation of energy, energy cannot be lost in a closed mechanical system. However, some energy may be converted to other forms, such as heat or sound, which may not be useful for the intended purpose.

5. How does friction affect the conservation of energy in a system?

Friction can cause some energy to be converted into heat, which is not useful for the intended purpose. This means that in a system with friction, the total mechanical energy may decrease over time, but the law of conservation of energy still holds true as the energy is only being transformed into a different form.

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