Solving for Tensions and Mass in a System of Forces

[c-murda]

[SOLVED] Finding Tensions IS SO FUN

Homework Statement

Find tesnions T1, T2, and T3 and M in figure attached...

Homework Equations

The Attempt at a Solution

To start i drew three FBD

A) for mass on left

Fm= T2-m*g = 0

B)the intersection

Fx = T3 cos 37 - T2 cos 63 = 0
Fy = T2 sin 63 + T3 sin 37 - T1 = 0

C) mass of box

F = T1 - mg


so...
C) box
T1 = (6.00kg)*(9.80m/s^2) = 58.8 N

B) Intersection
.799T3 - .454T2 = 0
.891T2 +.602T3 = 58.8N
.891T2 + .602[((.454/)(.799))*(T2))] = 58.8
1.23T2= 58.8N
T2= 58.8/1.23= 47.8N

T3 = ((.454/)(.799))*(T2); = ((.454/)(.799))*(47.8); T3 = 26.8

A) T2/g = m (47.8N)/(9.80 m/s^2) = m = 4.87kg

 

[Doc Al]

It's hard to tell from the diagram what those angles refer to. Are they the angles the strings make with the horizontal? Where does the angle 63 come from?

 

[c-murda]

It's hard to tell from the diagram what those angles refer to. Are they the angles the strings make with the horizontal? Where does the angle 63 come from?

the line is there merely just to show those angles...it was hard to tell from the original diagram so i put that line there...

 

[Doc Al]

You never answered my questions about the angles.

 

[c-murda]

You never answered my questions about the angles.

haha i did not read it all...lol

i assumed from the angle give it was attached to the horizontal...

 

[c-murda]

i got the 63 from the intersection when i drew the angle i added to make 180...37 plus 80 plus 63

 

[Doc Al]

i got the 63 from the intersection when i drew the angle i added to make 180...37 plus 80 plus 63

Sorry, still not clear to me. (Your diagram has the numbers floating about.) So are you saying:

The left string makes an angle of 80 to the horizontal?
The right string makes an angle of 37 to the horizontal?
The angle between the strings is 63?

 

[c-murda]

okay let's say there was a hypothetical line below the " V " where the 80 is...(implying that "v" angle would be 80 degrees), then the right string attaches to the horizontal at the top to make a 37 degree angle and the left string attaches to the pulley

below the 80degree angle and to the right would also be a 37 degree angle
below the 80 degree angle and to the left would be a 63 degree angle...

sorry I am not trying to make this confusing but the problem was drawn exactly how i have it...with number floating around and string attaching in weird places...

 

[Doc Al]

OK, now that I understand the angles (sorry about that!): Your work looks fine to me!

 

[c-murda]

my teacher took off one point because of T3 it needed to be rounded up... blah anyways...thanx for you help