# A Box is suspended by two strings, what is the tension?

• EthanVandals
In summary, two strings, T1 and T2, are anchored at 30 and 60 degrees to the horizon respectively, suspending a 100 kg block. The tension in the strings can be calculated using the equation T1 = mg/(tan(theta)cos(phi) + sin(theta)), with similar results for T2. By using the fact that the angles are complementary, the solution can be simplified.
EthanVandals
1. The problem statement, all variables, and given/known data
Suppose a block is suspended by two strings, one, T1, is anchored at 30 degrees to the horizon, the other, T2, at 60 degrees to the horizon. If the block weighs 100 kg, what is the tension in the two strings?
Assume that:
The 30-degree angle is Phi.
The 60-degree angle is Theta.
M = 100 kg
g = 10 m/s^s

## Homework Equations

(I had to create them myself, so they will be shown in the attempt section.)

## The Attempt at a Solution

This image details my attempt. I am fairly certain that I got the correct answers, but I would really appreciate confirmation as well as an explanation for why certain things may be sin or cos. Most of the formulas are ones the professor just gave to us in class, and instead of expecting us to know how to create them, he just wants us to memorize them, which I struggle with unless I know the basis behind it.

The key equation that you have is:

##T_1 = \frac{mg}{\tan(\theta) \cos(\phi) + \sin(\theta)}##

Which is very good!

In fact, if you then calculate a similar expression for ##T_2## you will see the symmetry of the solution.

To add to PeroK's answer, a useful thing to memorize is that if angles θ and φ are complementary, i.e. θ + φ = 90o, the sine of one is the cosine of the other. If you use this fact to express T1 in terms of one of the angles, say θ, your expression will simplify to a great extent. Do the same for T2 and you should recognize the expression relating the two tensions to the weight as something old and familiar.

## What is tension?

Tension is a force that is applied to an object in order to stretch or pull it. It is a type of force that occurs in any situation where two objects are interacting with each other and one is pulling on the other.

## How is tension calculated?

Tension is calculated by dividing the total force applied to an object by the cross-sectional area of the object. This results in a unit of force per unit area, such as pounds per square inch or newtons per square meter.

## What are the effects of tension?

Tension can cause objects to stretch, compress, or deform. It can also cause objects to break or snap if the force is too great. In some cases, tension can balance other forces and keep objects in a stable position.

## How does tension affect a suspended box?

In a suspended box, tension is responsible for holding the box in place and preventing it from falling. The tension in each string is equal to the weight of the box, ensuring that the box remains in equilibrium and does not move.

## What factors can affect the tension in a suspended box?

The tension in a suspended box can be affected by the weight of the box, the angle of the strings, and the strength and elasticity of the strings themselves. Other factors such as air resistance and external forces can also impact the tension in a suspended box.

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