Finding the inside angle using trigonometry

[Matt.D]

I'm new to trigonometry, but I think I know the basics - soh cah toa ect. If I want to find the angle of the pendulum first then I need to do:

Sin-1 * (opp / hyp)

However I haven't got the hypotenuse, but the adjacent. So am I right to firstly work out the hypotenuse by opposite2 + adjacent2 = hypotenuse2 and then square rooting the the anwer?

Or is there a simpler way I can calculate the inside angle without having to do that first?

The question I've been set for tonights homework is;

A 500g sphere is hung from an inextensible string 1.25m long and swings around to form a conical pendulum. The sphere move in a circular horizontal path of radious 0.75m Find the tension in the string.

Once I have the correct inside should I do the following:

t = mg/cos theta

t = ( 0.5 * 0.75) / cos theta

Thanks all :)

 

[dextercioby]

What hypothenuse are u talking about?The only one i can imagine is the string itself and it is given...1.25m...

Do you mean the one in the vector triangle??That is the weight of the sphere and is given as well...

Daniel.

 

[Matt.D]

Hi Daniel,

I don't think that its a vector triangle (we haven't covered that so I'm 99% sure that it isn't) so the 1.25m for the length is the same for the hypothenuse because its the same length - only its displaced to the side. right?

So if the hyp is 1.25 then to find the inside angle I need to do;

sin-1 * (0.75/1.25)

= 36.86989765
= 37degrees (rounded)

then do I do as I said in the original post, to find t?

 

[dextercioby]

The angle is okay...Then apply the second law of dynamics for the sphere and project it on the direction of the string...

Daniel.

 

[Matt.D]

Hi Dexter,

Thanks for your help.

Is the next part;

T = mg
cos 37

T = 0.5*9.8
cos 37

T = 4.9
0.798

T = 6.14N

Matt