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

[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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[Bystander]

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

 

[haruspex]

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?

By the way, please use thread titles which give some guidance as to the topic. It will help you get timely answers.

 

[CWatters]

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

 

[HalfLostAndSearching]

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.