# Tension Problem: Two boxes with two ropes

• awelex
In summary, the conversation discusses a problem involving two masses connected by a rope and a helicopter with acceleration. The aim is to find the tension in various ropes and the conversation includes equations and a solution attempt. The final answer is deemed correct and can be checked in a limiting case.
awelex
Hi,
here's a problem I did earlier today. I think I got it right, but I'd appreciate it if somebody could check. Also, is there a different way to solve this problem?

## Homework Statement

Two masses Ma and Mb are connected through a heavy rope with mass Mr. The top mass Ma is hanging from a from a massless rope that is that is attached to a helicopter that moves upwards with acceleration a. Find the tension in the top rope as well as the tensions in the bottom (heavy) rope.

I labeled the tension of the top rope T1, the tension of the heavy rope pulling downward on Ma T2.1, and the tension pulling upward on Mb T2.2.

## Homework Equations

For mass A: Fnet = Ma * a
--> T1 - T2.1 - Ma * g = Ma * a
--> T1 - T2.1 = Ma * a + Ma * g

For mass B: Fnet = Mb * a
--> T2.2 - Mb * g = Mb * a
--> T2.2 = Mb * a + Mb * g
This already gives us the tension from the heavy rope pulling upwards on the second mass.

For the entire system, without the top rope:
Fnet = (Ma + Mb + Mr) * a
--> T1 - (Ma + Mb + Mr) * g = (Ma + Mb + Mr) * a
--> T1 = (Ma + Mb + Mr) * (a + g)

I plugged this into the earlier equation with T1 and T2.1:

(Ma + Mb + Mr) * (a + g) - T2.1 = Ma * (a + g)
--> T2.1 = (Mb + Mr) * (a + g)

So we have:
T1 = (Ma + Mb + mr) * (a + g)
T2.1 = (Mb + Mr) * (a + g)
T2.2 = Mb * (a + g)

## The Attempt at a Solution

See above.

Is this correct?

That looks good.
You can check your answer in limiting case. When mass of the rope goes to zero, your answer gives the same result as massless rope.

Cool, thanks.

## 1. What is a tension problem?

A tension problem is a type of physics problem where the forces acting on an object or system are analyzed to determine the tension in ropes, strings, or cables connecting the object or system.

## 2. What are the key components of a tension problem with two boxes and two ropes?

The key components of a tension problem with two boxes and two ropes are the masses of the boxes, the angles of the ropes, and the tension forces in each rope. These components are used to calculate the overall tension in the system.

## 3. How do you set up and solve a tension problem with two boxes and two ropes?

To set up and solve a tension problem with two boxes and two ropes, you must first draw a free body diagram showing the forces acting on each box and the angles of the ropes. Then, you can use Newton's second law of motion and trigonometry to calculate the tension forces in each rope and the overall tension in the system.

## 4. What is the purpose of solving a tension problem with two boxes and two ropes?

The purpose of solving a tension problem with two boxes and two ropes is to determine the tension forces in each rope and the overall tension in the system. This information can be used to understand the stability and equilibrium of the system, as well as to determine the maximum weight each rope can support.

## 5. What are some real-life examples of tension problems with two boxes and two ropes?

Some real-life examples of tension problems with two boxes and two ropes include a person pulling a sled with two ropes, a crane lifting an object with two cables, and a bicycle rider pulling a trailer with two ropes attached to the bike. These situations involve multiple forces acting on the system and can be analyzed using tension problem principles.

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