Pendulum Speed at Different Heights

[xasuma]

Homework Statement

The pendulum shown (http://puu.sh/chwMZ/90f4b96fb1.png ) swings freely, turning around at a height of 10 cm above the lowest point in its swing. It has an unknown mass, but air resistance can be ignored.

a) Use energy conservation to find its speed at the lowest point of its swing.
b)What is the pendulum speed when it is at a height of only 1 cm above its lowest point?

Homework Equations

PE=mgh
V^2 = (2PE)/m

The Attempt at a Solution

I know I need to use the two equations above. But I don't know how. I can't understand how to do this problem. Therefore there is no attempted solution. I am not asking for a solution, I want to learn, but can someone explain to me what to do here?

 

[Matterwave]

Your second equation has basically already done most of the work for you, but you have to understand how to use it. In fact, I think that this equation will be more confusing to you than it will be helpful, so let's start with some simpler concepts.

Do you understand the concepts of Potential Energy and Kinetic Energy, and what IS this concept of "Energy conservation"?

 

[xasuma]

This is my understanding of it.
Potential energy is stored energy which has the potential to be released.
Kinetic energy is the energy an object has while in motion.
And energy conservation means that energy can change from potential to kinetic (or others) , since it can't be destroyed nor created.

I actually came up with the second equation by myself (I mean it wasn't given to me) .The problem I have is the mass. If the mass of the pendulum ball was given to me this would be no problem, but I can't get my head around it being unknown. I know that if air resistance is ignored, the acceleration would be 9.8m/s (if it were going straight down) but with the pendulum motion I get confused. I thought of the tension of the pendulum as well, drew a body diagram for the ball , but I just keep getting more confused.

Maybe the mass =1 , so it won't be important in this equation?
In that case I would say:
PE=9.8*0.1= 0.98N
v^2=(2*0.98)/1 = 1.96
v=1.4 m/sI don't really know though.

 

[Simon Bridge]

PE=9.8*0.1= 0.98N

PE has units of energy: "Joules" (J); "Newtons" (N) are units of force.
You seem to have written PE = gh ... gh has units of m^2/s^2 - not N or J.
This is a clue and should clear up your confusion.

This is one place where doing all the algebra before you put numbers into the equations really pays off.
You've already figured out that all the gravitational PE lost at the top of the arc goes into kinetic energy at the bottom.
So just write out <the formula for kinetic energy> = <the formula for potential energy> and then cancel terms.

 

[xasuma]

I see,
so I got:
1/2mv^2 = mgh , solve for v (speed)

v^2 = 2gh
v^2 = 2*9.8*0.1
v= 1.4 m/s

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Now for B. The speed of the pendulum 1 cm above the lowest point.
I just changed 'h' from 0.1 to 0.09, did the same calculation as above and got:

v= 1.33 m/s

Did I do it right? I believe I get it :)

 

[Simon Bridge]

It came out with the same answer - just for better reasons.
Well done - the thing about laying it out clearly like that is you end up with more confidence in your results.
Also notice that doing the algebra first gives you an equation that you can use in the next question with no extra work.

You can reality check your answers by thinking about the physics ... the v you calculated before was at the bottom of the swing - do you expect that the speed is faster or slower higher up? Is what you got consistent with that?