Question about Tension 100 identical blocks

In summary, the problem involves 100 identical blocks connected by massless strings on a frictionless surface. The first block is pulled with a force of 100 N. The tension in the string connecting block 100 to block 99 is unknown, but can be determined by considering the entire set of blocks as a single mass being pulled. The same approach can be used to find the tension in the string connecting block 50 to 51. However, if there is a coefficient of friction, this would need to be taken into account when determining the tension in the strings.
  • #1
sona1177
173
1
Each of 100 identical blocks sitting in a frictionless surface is connected to the next block by a massless string. The first block is pulled with a force 100 N.

a) what is the tension in the string connecting block 100 to block 99

B) what is the tension in the string connecting block 50 to 51?

I don't know how to do this. The only equation I got was T2-T1=ma for box 99 where T2 is the tension string attaching to box 98 and T1 is the tension in the string attached to 100. Also for box 100 I got -T=ma and plugged this into the equation -100 + T=ma and got T=50 N but this is wrong for part A and is supposed
To be the answer for part B but I don't see why. Can you please explain how to do this?
 
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  • #2
Assuming the string doesn't stretch, all the masses will have the same acceleration. So, think of the entire set of blocks as a single mass being pulled and solve for the acceleration. Then you can determine the string tension between any of the blocks by considering all blocks upstream to be a single mass and all blocks downstream to be a single mass, thereby having a two block system.
 
  • #3
Does this picture make it any easier? All the blocks accelerate the same but you can combine blocks.

blocks.JPG



oops, edit, someone answered whilst I was drawing.
 
  • #4
So if there were a coefficient of friction of say 0.1 in this problem, then the 99 blocks together would produce a friction force of 0.1 x 99M x g and the one block to the right would produce a friction force of 0.1 x M x g.
And each of these two friction forces would be the amount that is added to its corresponding equation. Right?
 
  • #5


I would approach this problem by first understanding the concept of tension. Tension is a force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In this scenario, the tension in the string connecting the blocks is equal throughout the entire string since it is massless and the blocks are identical. This means that the tension in the string between block 99 and block 98 is the same as the tension between block 98 and block 97, and so on.

Now, let's look at the first part of the question. We know that the first block is being pulled with a force of 100 N. This means that the tension in the string attached to block 100 is also 100 N, as the tension is equal throughout the string. However, since block 99 is connected to block 100 by the string, the tension in the string connecting these two blocks must also be 100 N. This is because if the tension was less than 100 N, block 99 would not be able to stay in place and would start accelerating towards block 100.

For the second part of the question, we are asked to find the tension in the string connecting block 50 to block 51. Again, we know that the tension in the string is equal throughout the entire string, so the tension in the string connecting these two blocks must also be 100 N. This is because if the tension was less than 100 N, block 50 would not be able to stay in place and would start accelerating towards block 51.

In summary, the tension in the string connecting block 100 to block 99 and the tension in the string connecting block 50 to block 51 is both 100 N. This is because the tension in a massless string is equal throughout the entire string. I hope this explanation helps you understand the concept of tension and how to approach this problem.
 

1. What is tension?

Tension is a force that occurs when an object is pulled or stretched. It is often referred to as a pulling force and is measured in units of Newtons (N).

2. How is tension different from compression?

Tension and compression are both types of forces that act on objects, but they act in opposite directions. Tension pulls on an object, while compression pushes on an object.

3. How is tension related to the 100 identical blocks?

The tension in a system of 100 identical blocks is a result of the weight of the blocks pulling down on each other. As more blocks are added to the stack, the tension increases because there is more weight pulling down on the bottom block.

4. What factors affect the tension in a system of 100 identical blocks?

The tension in a system of 100 identical blocks is affected by the weight of each block, the force applied to the stack, and the stability of the stack. The taller the stack, the more tension there will be.

5. How is tension used in real life?

Tension is used in many real-life applications, such as in bridges, cranes, and suspension systems. In these cases, tension is used to support the weight of the structure and prevent it from collapsing or breaking under the force of gravity.

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