Forces, involving tension and a pendulum

[://Justice]

Homework Statement

A ball of weight 5 N is suspended by two strings as shown [linked below].
(a) Draw and label all forces that act on the ball.
(b)Determine the magnitude of each of the forces indicated in part (a).

Suppose that the ball swings as a pendulum perpendicular to the plane of the page [or, in this case, computer screen. As if it is swinging towards, and away from you], achieving a maximum speed of .6 m/s during it's motion.

(c) Determine the magnitude and direction of the net force on the ball as it swings through the lowest point in it's motion.

I think I understand (a) well enough. I need a little help on (b) (a bit of a poke in the right direction, I suppose), and I am just really lost on (c). Thanks.

Below is my best recreation of the diagram I have been provided with, created in Google Docs.
https://docs.google.com/drawings/edit?id=1uH2B3r1d-COC1TYU17Itg1kLf4C7v1OHZtn6QS0huzg&hl=en"

Homework Equations

$$\sum$$F_net = ma

The Attempt at a Solution

(a) So, free body diagram is easy enough. Could you please check it. It is to the right in the GoogleDoc provided at the top.

(b) Okay, a bit more complicated. So, I have the degree of the string, the length of the string, and the weight of the ball. I also know that gravity is constant, at 9.81 m/s^2. Therefore, m_bg = (5N)(9.8m/s^2) [or would you have to convert 5N to kg somehow?). Then, I know that T1 + T2 = mg. So... stuck... Now I figure that somehow the degrees and lengths come into play, but I really don't know how...

(c) I really do not understand this problem, or the concept behind it. I don't think we have actually been taught how to do this... Still, I am sure that it is quite obvious and understandable once I know it... SO, at the lowest point, the acceleration is... 0? in the y-direction?

SO if you could please, please help me with these I will be forever grateful, haha. Thank you in advance

 

[The legend]

for part b)
you are already given the weight of the ball = 5N so no need to multiply by g..
Now
the equation will look like this
T1*sin53 + T2*sin37=mg=5N
and you will also get another equation assuming the ball is in equilibrium

T1 *cos53=T2*cos37..

Get an idea?

 

[://Justice]

AH, now it all flashes back to me! haha. Thanks. Good old systems of equations and such.
Really not sure if I did this right. Basically, after setting the first equation to equal T2, I got this:
2(T2)= (5N*Cos(theta1)) / (Cos(theta2)*Sin(theta1))+Sin(theta2)) wow, long...
And so I got T2 = 1.213N, and then plugging that into T1 = (T2*Cos(theta2)) / Cos(theta1), I got T1 = 1.601N
But does that make sense? Should T1 + T2 = 5N ?? Confused...

 

[The legend]

an easier way i think would be
find the value of T1 in terms of T2 from the second equation... then just plug in the values in the first equation and voila!

 

[://Justice]

Which, I thought, was essentially what I did...
T1 = T2*Cos(37) / Cos(53), then plug that in...
(T2*Cos(37) / Cos(53))*Sin(53)+T2*Sin(37)=5N
So, then set it equal to T2, as I did above. And then you have your answer... which I got as 1.213N. Where did I go wrong?

 

[The legend]

you went wrong in your calculations... try doing them again.(if you need use a calculator)
I get T2=approx 3.01

 

[://Justice]

But would 3.01 not equal 2T2? but I kind of get it...

 

[The legend]

T2 (Cos(37) * tan(53)+sin(37)) = 5
T2(1.66) = 5
T2 = 3.01

now?

 

[://Justice]

AH, I get it now... Sorry I'm so slow... Okay, thanks. Then T1 is easy enough. Thanks.
Haha... now (c)... I have absolutely no idea where to begin...

 

[The legend]

the max speed 0.6m/s will be attained on the mean position..
for further part you need basic knowledge of circular motion... do you know anything about it?

 

[://Justice]

I know it's no excuse, but I swear I have a horrible physics teacher... (by the way, this isn't just some new homework, but a take home test (so we are supposed to already know all of this)).
I think I probably have a basic knowledge of it, I just do not know it... basically, we have probably been taught somewhere, but he never actually told us "This is circular motion and this is how you do it."
Umm... so, the direction should probably be the easiest of the two, no? Or would it require the magnitude?