Tension in Strings: Solving a .5kg Problem

[aeroengphys]

For homework, I was given the following problem:

A .5kg hangs from two strings at the angles shown. The longer string is .5m long.
(a) Determine the tension in each string.

(see attachment for diagram)Can you tell me how this looks...

1st I broke everything into x and y components (ie Tlx, Tly, Trx, Try) then i did the following:

x
ΣF=0N
Tlx=Trx
Tlcos(60)=Trcos(25)
Tl=Trcos(25)/cos(60) y
ΣF=0N
Tly + Try = 5N
Tlsin(60)+Trsin(25) = 5N
(Trcos25/cos60)*sin60 + Trsin25= 5N
Tr((cos25*sin60)/cos60) + sin25= 5N
Tr = (5N - sin25)/((cos25*sin60)/cos60)
Tr = 2.92NThen...I went back to my x components and plugged in Tr and solved for Tl as shown:

Tl = (2.92N)(cos25)/cos(60)
Tl = 5.29N

Hopefully that's right...Thanks in advance for letting me know.

 

[Doc Al]

I didn't check your arithmetic, but your method is perfect. (Are you taking g = 10 m/s^2? Often 9.8 m/s^2 is used.)

 

[aeroengphys]

In AP Physics B, they tell you to use 10m/s² since on the multiple choice you won't be able to use a calculator.

 

[Doc Al]

In AP Physics B, they tell you to use 10m/s² since on the multiple choice you won't be able to use a calculator.

That's cool. As long as you are doing so on purpose.

Do they really expect you to calculate trig functions--like cos(25)--without a calculator?

 

[rsk]

calculations involving g will undoubtedly appear on the non-calculator paper.Questions involving sin25 are highly unlikely to.

sin/cos of 0, 30, 45, 60 and 90 maybe

 

[aeroengphys]

This is a part II question, so technically you could probably use 9.8, but my teacher told us to just keep using 10. As for trig functions, they use sin/cos of 30/45/60/90 on the AP exam.

 

[goalieguy]

the AP equation sheet includes sin/cos/tan of selected angles (0,30,45,60,90).
They don't use other angles in the non-calculator section

 

[rsk]

This is a part II question, so technically you could probably use 9.8, but my teacher told us to just keep using 10.

They couldn't demand you use different values on different papers - that's just asking for confusion.

 

[nealh149]

It's always good to use 10 m/s^2 anyway for quick checks (eg multiple choice) because it gives accuracy up to two places.