Solving Energy Conservation for Pendulum Movement

[jim the duke]

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

 

[Doc Al]

Why not use conservation of energy.

 

[jim the duke]

How would i use it to get the speeds at intervals though?

 

[Doc Al]

How would i use it to get the speeds at intervals though?

Figure out the height of the pendulum at each of those points.

 

[jim the duke]

I've already worked out the swing heights at any given interval, its the speed in m/s i need.
Thanks

 

[Doc Al]

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?

 

[jim the duke]

Pass?

 

[jim the duke]

v=SQRT(2*KE/m).

 

[Doc Al]

v=SQRT(2*KE/m).

OK, that how to get velocity from KE.

What's an expression for the total energy of the pendulum?

 

[jim the duke]

E = mgL[1 - cos(θ0)] ?

 

[Doc Al]

E = mgL[1 - cos(θ0)] ?

That will give you the gravitational PE, measured from the lowest point.

What's the total energy?

 

[jim the duke]

Sorry i don't know

 

[Doc Al]

Sorry i don't know

Look up total mechanical energy (and conservation of energy) in your textbook.

 

[jim the duke]

Tme = pe + ke

 

[Doc Al]

Tme = pe + ke

Good!

That's conserved as the pendulum moves.

 

[jim the duke]

Ok so now what - total mech en = pot en + kin en
What step do i take next?

 

[Doc Al]

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.

 

[jim the duke]

How do i get the speed from that equation though?

 

[Doc Al]

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.)

 

[jim the duke]

But i still have no figure for Mass so i cannot calc - KE = 1/2mv^2

 

[Doc Al]

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.

 

[jim the duke]

Im lost, i give up

 

[Doc Al]

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.

 

[jim the duke]

V= SQRT 2gl(1-cos∅max)