Pendulumn Problem (did i do this correctly?)

[Lori]

Homework Statement

find the speed of the object as it goes through the lowest point on its trajectory given that a pendulum is made by letting a 2.0 kg object swing at the eng of a string of length 1.5

Homework Equations

h= mg(L-Lcostheta)
mgh = .5mv^2
[/B]

The Attempt at a Solution

mgh = .5mv^2 (conservation of energy)[/B]
(2)(9.81)(0.20096) = .5(2)v^2
solve for v, v = 1.98 m/s

 

[Charles Link]

The statement of the problem is incomplete. Information is needed on how far the pendulum swings (in angle $\theta$). Presumably the length $L=1.5$ m.

 

[Lori]

The statement of the problem is incomplete. Information is needed on how far the pendulum swings (in angle $\theta$). Presumably the length $L=1.5$ m.

Oops! I left out the angle. It says 30degrees is the max angle that string makes

 

[Charles Link]

Can you compute how high up ($h$) that the pendulum is at $\theta=30^o$, compared to when $\theta=0^o$ and $h=0$? $\\$ Note:The equation that you supplied for $h=mg (L-L \cos(\theta))$ has an $mg$ that doesn't belong in the equation. Meanwhile, if you draw a good diagram, you should be able to compute $h$ without using a formula.

 

[Lori]

Can you compute how high up ($h$) that the pendulum is at $\theta=30^o$, compared to when $\theta=0^o$ and $h=0$? $\\$ Note:The equation that you supplied for $h=mg (L-L \cos(\theta))$ has an $mg$ that doesn't belong in the equation. Meanwhile, if you draw a good diagram, you should be able to compute $h$ without using a formula.

I didn't really use that formula. I just figured it out that it i needed to find the height to calculate mgh. I've drawn the picture but it is difficult to post on here~ I think i know what you mean though! I think i mean to say that i calculated mgh and found h by L-Lcostheta. Sorry for the confusion!

 

[Charles Link]

Very good. The string makes a $30^o, 60^o, 90^o$ triangle if you draw one vertical line down the middle, and the hypotenuse is along the string that is pulled $30^o$ from center. The first length you need to compute is how far down the string is (from the point where the pendulum swings from), if you go straight across horizontally to the middle of the pendulum when the pendulum is $30^o$ from the center. It would be easier if we had a diagram...I'm hoping you get the answer that the vertical length is $L \cos(30^o)$.