# Calculating Tension in a Revolving Mass: Homework Solution

• sunnnystrong
In summary, the figure shows two wires attached to a 970g mass revolving in a horizontal circle at a constant speed of 7.5 m/s. The wires are both 1m long and attached to a pole in an equilateral triangle with a radius of cos(30 degrees). Using the equation ∑F = m*a, the tensions in the upper and lower wires (T1 and T2) can be calculated by solving for T1 in the y-direction and plugging that value into the equation for the x-direction. Thus, the tension in the upper wire is 46 N and the tension in the lower wire is 26.868 N.
sunnnystrong

## Homework Statement

The figure shows two wires that are tied to a 970g mass which revolves in a horizontal circle at a constant 7.5 m/s. What is the tension in the upper wire?

The wires are both 1m long, and are attached to a pole. The radius is cos(30 degrees). It's an equilateral triangle.

∑F = m*a

## The Attempt at a Solution

[/B]
∑Fy = 0.
∑Fx = (m*v^2) / r

First I looked at the forces in the y-direction. Down = negative.
The upper rope = T1. The lower rope = T2.

(.5)T1 - (.5)T2 - mg = 0
*Solve for T1*
T2 + 2*m*g = T1 // EQN 1

Next, in the X-Direction. Inward = positive.

T1cos(30) + T2cos(30) = (m*v^2)/r
Plug in value for T1 to solve for T2.
2*T2*cos(30) + 2*m*g*cos(30) = (m*v^2)/r
[(m*v^2)/r - 2*m*g*cos(30) ] / (2cos(30) = T2
T2 = 26.868 N

Plug into EQN 1 and I got T1 = 46 N

Looks good.

sunnnystrong
gneill said:
Looks good.
Thank you!

## 1. What is a tension problem?

A tension problem is a type of physics problem that involves calculating the force exerted on an object by a string, rope, or cable that is pulling on the object.

## 2. How do I solve a tension problem?

To solve a tension problem, you will need to use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. You will also need to use the formula for tension, which is T = mg + ma, where T is the tension force, m is the mass of the object, g is the acceleration due to gravity, and a is the object's acceleration.

## 3. What are the common mistakes when solving a tension problem?

One common mistake when solving a tension problem is forgetting to include the weight of the object when calculating the tension force. Another mistake is using the wrong units, such as using kilograms instead of Newtons for force. It is also important to pay attention to the direction of the tension force, as it can be different depending on the problem.

## 4. How can I check my work for a tension problem?

To check your work for a tension problem, you can use the principle of conservation of energy. This means that the total energy of the system (including the tension force) should remain constant throughout the problem. You can also double check your calculations and units to make sure they are correct.

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

Tension problems are commonly used in engineering and construction to determine the strength of materials and structures. They are also used in sports, such as rock climbing, to calculate the tension force needed to support a climber's weight. Additionally, tension problems are important in understanding the mechanics of pulleys, cranes, and other machines that use tension to lift or move objects.

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