Calculating the Speed of a Pendulum Using the Law of Conservation of Energy

[agentd00nut]

hi, i can't figure out which equation to use could anyone give me a nudge in the right direction with a formula please? thank you

A 3.3 m long pendulum is released from rest when the support string is at an angle of 24° with the vertical. What is the speed of the bob at the bottom of the swing?

 

[quantumdude]

Well, I'll tell you this much: If you're looking for a formula then you're not thinking about it right.

We have a policy here, and that is that you are supposed to show how you started and where you got stuck. So, what do you think about this problem?

 

[agentd00nut]

oh sorry, I am new here, well i missed the lecture for this in class so I am kinda just poking in the dark trying to use my book and i came up with (3.3/9.8)cos(24) and i have no idea what to do with any of this, really frustrating, then i though maybe i could use something about KE being transferred to PE and conservatiopn of energy but i have no idea

 

[quantumdude]

then i though maybe i could use something about KE being transferred to PE and conservatiopn of energy but i have no idea

Nah, you've got some idea, because you stated the correct approach here: You are supposed to use conservation of energy.

You need to write down expressions for the total energy of the pendulum bob at the top of its swing, and at the bottom of its swing. Then use the fact that energy is conserved.

So, start at the top of the swing. Can you write down an expression for the total energy at that point?

 

[agentd00nut]

well KEi=0 since there is no movement, PEi = mgh so I am thinking 3.3cos(24)=h, but it is massless so i don't know what to do with it, and at the end, PE=0 and KE= .5mv^2, i don't know what to do when it is massless

 

[quantumdude]

well KEi=0 since there is no movement,

Right.

PEi = mgh so I am thinking 3.3cos(24)=h,

You need to check your geometry here, preferably by drawing a picture. Since you say later that the height of the bob at the bottom of the swing is h=0 (which is a good choice), the height of the bob at the top will certainly not be h=3.3cos(24).

but it is massless so i don't know what to do with it,

You can't assume that it is massless. So put in an "m" for the mass.

(Once you set up the law of conservation of energy, you will find that the mass cancels out and so you do not need to know it.)

and at the end, PE=0 and KE= .5mv^2,

Right.

 

[agentd00nut]

thank you so much for the help, i can get it from here