What is the Tension in Each String for a Hanging Ball?

[dolerka]

Homework Statement

A ball of mass 0.850 kg is dangling as shown. The angle created with String 1 and ceiling is 30 degrees. The angle created with the second and the ceiling is 45 degrees. What is the tension in each string?

Homework Equations

F=ma

The Attempt at a Solution

T1=tension in string 1
T2=tension in string 2
W=weight of ball

I determined the the x and y acceleration to be zero. T1y+T2y=0. and T1x+T2x+W=0. i then used trigonometric identities.

T1y=T1sin(120)
T2y=T2sin(45)

T1x=T1cos(120)
T2x=T2cos(45)
W=8.33N

i then did substitution with the formulas and i found the tension in string 1 to be 6.10 i know this to be correct. and substituting in for the second tension i get 4.31 but i am being told that this is wrong so what exactly am i doing wrong?

 

[gneill]

T1=tension in string 1
T2=tension in string 2
W=weight of ball

I determined the the x and y acceleration to be zero. T1y+T2y=0. and T1x+T2x+W=0. i then used trigonometric identities.

T1y=T1sin(120)
T2y=T2sin(45)

T1x=T1cos(120)
T2x=T2cos(45)
W=8.33N

i then did substitution with the formulas and i found the tension in string 1 to be 6.10 i know this to be correct. and substituting in for the second tension i get 4.31 but i am being told that this is wrong so what exactly am i doing wrong?

Suppose, for an experiment, the ball was substituted with one of twice the weight. What would be the tension in the strings?

 

[tiny-tim]

welcome to pf!

hi dolerka! welcome to pf!

(have a degree: ° and try using the X₂ icon just above the Reply box )

I determined the the x and y acceleration to be zero. T1y+T2y=0. and T1x+T2x+W=0. i then used trigonometric identities.

T1y=T1sin(120)
T2y=T2sin(45)

T1x=T1cos(120)
T2x=T2cos(45)
W=8.33N

if y is up, then your W is in the wrong equation

and whyever are you using 120° ?

 

[dolerka]

hi dolerka! welcome to pf!

(have a degree: ° and try using the X₂ icon just above the Reply box )if y is up, then your W is in the wrong equation

and whyever are you using 120° ?

bleh yes first time post. and the equation read T1y+T2y=0 should be T_1x+T_2x=0. and T1x+T2x+W=0 should be T_1y+T_2y+W=0. also i used 120^o only because my book gives an example of a similar problem and also does this but that example on solved for one side.

 

[Kartikc]

the system is in equilibrium.
draw components of both the tensions...we get
T2sin30+T1sin45=ma...1
T2cos30=T1cos 45 ...2
solve de 2 eq. to get T1 and t2...please correct me...if i m wrong...i m new here!

 

[tiny-tim]

welcome to pf!

hi Kartikc! welcome to pf!

(try using the X₂ icon just above the Reply box )

the system is in equilibrium.
draw components of both the tensions...we get
T2sin30+T1sin45=ma...1
T2cos30=T1cos 45 ...2
solve de 2 eq. to get T1 and t2...

yes, that looks fine

(with "mg" of course)