# Homework Help: Pendulum bobs

1. Dec 2, 2012

### jim the duke

1. The problem statement, all variables and given/known data

Conservation of energy: looking for equations to solve the following

2. Relevant 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

3. 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

2. Dec 2, 2012

### Staff: Mentor

Why not use conservation of energy.

3. Dec 2, 2012

### jim the duke

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

4. Dec 2, 2012

### Staff: Mentor

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

5. Dec 2, 2012

### jim the duke

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

6. Dec 2, 2012

### Staff: Mentor

How would you express conservation of mechanical energy for the pendulum?

7. Dec 2, 2012

Pass?

8. Dec 2, 2012

### jim the duke

v=SQRT(2*KE/m).

9. Dec 2, 2012

### Staff: Mentor

OK, that how to get velocity from KE.

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

10. Dec 2, 2012

### jim the duke

E = mgL[1 - cos(θ0)] ?

11. Dec 2, 2012

### Staff: Mentor

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

What's the total energy?

12. Dec 2, 2012

### jim the duke

Sorry i dont know

13. Dec 2, 2012

### Staff: Mentor

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

14. Dec 2, 2012

### jim the duke

Tme = pe + ke

15. Dec 2, 2012

### Staff: Mentor

Good!

That's conserved as the pendulum moves.

16. Dec 2, 2012

### jim the duke

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

17. Dec 2, 2012

### Staff: Mentor

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. Dec 3, 2012

### jim the duke

How do i get the speed from that equation though?

19. Dec 3, 2012

### Staff: Mentor

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. Dec 3, 2012

### jim the duke

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