Solving Energy Conservation for Pendulum Movement

In summary: When you write your energy conservation equation, you'll see that mass (which appears in both the PE and KE terms) will drop out.
  • #1
jim the duke
23
0

Homework Statement



Conservation of energy: looking for equations to solve the following

Homework Equations



A pendulum with length l = 0.50 m and with a negligible mass. The string is attached to a fixed point A and the pendulum swings in a vertical plane.

The pendulum has a speed v = 2.15 m s–1 at the lowest point of its swing.

I need to work out the pendulums speed at intervals so 10,20,30,40 degrees

The Attempt at a Solution


I have already calculated the time period of the swing to T = 2 pi sqrt l/g, which means T= 1.59s, also the height of the swing from lowest point to end is 0.49m

Any help would be great, thanks
 
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  • #2
Why not use conservation of energy.
 
  • #3
How would i use it to get the speeds at intervals though?
 
  • #4
jim the duke said:
How would i use it to get the speeds at intervals though?
Figure out the height of the pendulum at each of those points.
 
  • #5
I've already worked out the swing heights at any given interval, its the speed in m/s i need.
Thanks
 
  • #6
jim the duke said:
I've already worked out the swing heights at any given interval, its the speed in m/s i need.
How would you express conservation of mechanical energy for the pendulum?
 
  • #7
Pass?
 
  • #8
v=SQRT(2*KE/m).
 
  • #9
jim the duke said:
v=SQRT(2*KE/m).
OK, that how to get velocity from KE.

What's an expression for the total energy of the pendulum?
 
  • #10
E = mgL[1 - cos(θ0)] ?
 
  • #11
jim the duke said:
E = mgL[1 - cos(θ0)] ?
That will give you the gravitational PE, measured from the lowest point.

What's the total energy?
 
  • #12
Sorry i don't know
 
  • #13
jim the duke said:
Sorry i don't know
Look up total mechanical energy (and conservation of energy) in your textbook.
 
  • #14
Tme = pe + ke
 
  • #15
jim the duke said:
Tme = pe + ke
Good!

That's conserved as the pendulum moves.
 
  • #16
Ok so now what - total mech en = pot en + kin en
What step do i take next?
 
  • #17
jim the duke said:
Ok so now what - total mech en = pot en + kin en
What step do i take next?
Energy is conserved. It remains constant:

E1 = E2

PE1 + KE1 = PE2 + KE2

Let position 1 be the lowest point; position 2 being any other position you need to solve for.
 
  • #18
How do i get the speed from that equation though?
 
  • #19
jim the duke said:
How do i get the speed from that equation though?
Once you have the KE at each point, then you can get the speed using KE = 1/2mv^2. (See the equation you showed in post #8.)
 
  • #20
But i still have no figure for Mass so i cannot calc - KE = 1/2mv^2
 
  • #21
jim the duke said:
But i still have no figure for Mass so i cannot calc - KE = 1/2mv^2
When you write your energy conservation equation, you'll see that mass (which appears in both the PE and KE terms) will drop out. You won't need it.
 
  • #22
Im lost, i give up
 
  • #23
jim the duke said:
Im lost, i give up
You know the expressions for PE and KE, just plug them into the conservation of energy equation in post #17.
 
  • #24
V= SQRT 2gl(1-cos∅max)
 

FAQ: Solving Energy Conservation for Pendulum Movement

What is energy conservation in the context of pendulum movement?

Energy conservation refers to the principle that states energy cannot be created or destroyed, but can only be transferred or transformed from one form to another. In the context of pendulum movement, this means that the total amount of energy in the system (the pendulum) remains constant, with energy being transferred between kinetic and potential forms as the pendulum swings back and forth.

How does energy conservation affect the movement of a pendulum?

Energy conservation plays a crucial role in determining the movement of a pendulum. As the pendulum swings, potential energy is converted into kinetic energy and vice versa. This allows the pendulum to continue swinging without losing energy, resulting in a perpetual motion.

Can energy conservation be applied to all types of pendulum movements?

Yes, energy conservation can be applied to all types of pendulum movements, including simple, compound, and physical pendulums. As long as there is no external energy input or friction, the total energy of the pendulum will remain constant.

How can energy conservation be used to optimize pendulum movement?

Energy conservation principles can be used to optimize pendulum movement by adjusting the length and weight of the pendulum. By finding the right combination, the pendulum can maintain a constant energy level and achieve a more precise and regular swing.

What are some real-world applications of energy conservation in pendulum movement?

Energy conservation in pendulum movement has several real-world applications, including timekeeping devices such as grandfather clocks and metronomes. It is also used in seismometers to measure earthquake activity and in pendulum-powered toys. Additionally, the principles of energy conservation in pendulum movement are applied in mechanical engineering and physics experiments.

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