# Find Tension of Rope in Two Blocks System: 5kg, 7kg, 4kg, 200N

• legendknight
You can use F = ma to calculate the acceleration. From there, you can calculate the tension at each point using the formula T = m*a, where m is the mass of the section of rope and a is the acceleration. In summary, to find the tension at the top, lower, and midpoint of the rope, you will need to use the formula T = m*a, where the mass and acceleration are calculated using F=ma and the given masses and force. Remember to show all forces in a force diagram for each section of the rope.
legendknight

## Homework Statement

two blocks of masses 5kg and 7kg are connected by uniform rope of mass 4kg.an upward force Force=200N is applied on the system .How to find the tension at top, lower and midpoint of the rope

## Homework Equations

(take g=10m/second square).I only know this.Please tell me the formula to calculate the tension at top,lower and midpoint of the rope.

## The Attempt at a Solution

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You've got a start on your force diagram. It looks good as far as you've gone. Finish it. First hint: F = ma.

As Bystander writes, you need to show all the forces in the diagram. However, I would suggest you do this with separate free body diagrams for each part on which a force of interest acts directly. How many such components are there?

The trick is to realize that everything must accelerate at the same rate because they are tied together.

To calculate the tension at various points in the rope, we can use the equation T = mg + ma, where T is the tension, m is the mass of the block on either side of the rope, g is the acceleration due to gravity (10 m/s^2), and a is the acceleration of the system.

In this case, the system is experiencing an upward force of 200N, so we can calculate the acceleration using Newton's second law, F = ma. Therefore, a = F/m = 200N / (5kg + 7kg + 4kg) = 10/16 = 0.625 m/s^2.

At the top of the rope, we have the 5kg block, so T = (5kg)(10 m/s^2) + (5kg)(0.625 m/s^2) = 50N + 3.125N = 53.125N.

At the midpoint of the rope, we have the 7kg block, so T = (7kg)(10 m/s^2) + (7kg)(0.625 m/s^2) = 70N + 4.375N = 74.375N.

At the lower end of the rope, we have the 4kg mass, so T = (4kg)(10 m/s^2) + (4kg)(0.625 m/s^2) = 40N + 2.5N = 42.5N.

Therefore, the tension at the top of the rope is 53.125N, at the midpoint is 74.375N, and at the lower end is 42.5N.

## What is the formula for finding the tension of a rope in a two block system?

The formula for finding the tension of a rope in a two block system is T = (m1 * g * a) / (m1 + m2), where T is the tension, m1 and m2 are the masses of the blocks, g is the acceleration due to gravity, and a is the acceleration of the system.

## What units are used for the masses and tension in this system?

The masses are typically measured in kilograms (kg) and the tension is measured in Newtons (N).

## Can the tension be negative in this system?

No, the tension cannot be negative as it is a force and has a magnitude. It can only have a positive or zero value.

## What is the role of the acceleration in the formula for tension?

The acceleration in the formula represents the net acceleration of the system. It takes into account the forces acting on the system, such as the gravitational force and any external forces, to determine the tension in the rope.

## How do I determine which block has the greatest tension in this system?

In this system, the block with the largest mass will typically have the greatest tension. However, if the system is accelerating, the block with the smallest mass may have a greater tension due to the acceleration of the system.

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