Each of 108 identical blocks sitting on a frictionless surface is connected to the next block by a massless string. The first block is pulled with a force of 108N. What is the tension in the string connecting block 108 to block 107?
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Use the same method.
To determine the tension in the string connecting block 108 to block 107, we can apply Newton's second law of motion.
1. First, let's consider the forces acting on block 108. There are two forces: the pulling force of 108N and the tension in the string connecting it to block 107.
2. The pulling force acts in the left direction, and we'll represent it as F_pull. The tension in the string connecting block 108 to block 107 acts in the right direction and will be denoted as T_108-107.
3. Because the blocks are connected by massless strings, the tension is the same throughout the entire string. Therefore, the tension between block 108 and 107 (T_108-107) is equal to the tension between block 107 and 106, and so on.
4. According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration. In this case, the mass of each block is not provided, but it cancels out when considering the acceleration.
5. Since the surface is frictionless, there is no frictional force acting on the blocks.
6. Now, let's analyze the forces acting on block 107. There are three forces to consider: the tension in the string connecting it to block 106 (T_107-106), the tension in the string connecting it to block 108 (T_108-107), and the tension in the string connecting it to block 106 (T_107-106).
7. The tension T_107-106 is transmitted from block 108 to block 107 through the string, so it acts in the opposite direction of T_108-107.
8. Applying Newton's second law to block 107, we can write the following equation:
T_107-106 - T_108-107 = 0
9. From the equation in step 8, we can conclude that T_107-106 is equal to T_108-107. Both tensions are the same.
Therefore, the tension in the string connecting block 108 to block 107 is 108N.