# Tension in Strings: Solving a .5kg Problem

• aeroengphys
In summary, the student was asked to calculate the tension in each string based on the given information. The student used trig functions to find the tension in each string.
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.

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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.)

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.

aeroengphys said:
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?

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

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.

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

aeroengphys said:
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.

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.

## 1. What is tension in strings?

Tension in strings is the amount of force being applied to a string that causes it to stretch or become taut. It is typically measured in units of Newtons (N) or pounds (lbs).

## 2. How do you calculate tension in strings?

The formula for calculating tension in strings is T = mg, where T is tension, m is mass, and g is the acceleration due to gravity (9.8 m/s²). In this case, the mass is .5kg, so the tension would be 4.9N.

## 3. What is the relationship between tension and frequency?

Tension and frequency are directly proportional. This means that as tension increases, frequency also increases. Similarly, as tension decreases, frequency decreases. This relationship is known as Hooke's Law.

## 4. How does the length of the string affect tension?

The length of the string does not directly affect tension. However, as the length of the string increases, the mass of the string also increases, resulting in a higher tension. This is because a longer string has more mass to stretch and thus requires more force to create the same amount of tension.

## 5. What are some real-world applications of tension in strings?

Tension in strings is used in a variety of real-world applications, such as musical instruments (where the tension in strings produces sound), suspension bridges (where the tension in cables supports the weight of the bridge), and even in surgical procedures (where tension in sutures holds wounds together).

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