Question

In scenario 1, a person pulls with a force F on a string of length 2d that is connected to a spring scale. The other end of the spring scale is connected to a post by a string of length d . In scenario 2, the person pulls on the string of length $2d$ with a force of F, and a second person stands where the post was in scenario 1, and also pulls with a force of F. If the spring scale reads $50\;{\rm{N}}$ in scenario 1, what does the spring scale read in scenario 2?

Answer 1

In this question, a person stands and stretches the length of the wire. We see that in scenario 1, the scale reads $50\;{\rm{N}}$ with a person stretching the string and in scenario 2, the other person pulls the string with the same force. So, there is the same force acting on both scenarios.

Complete step by step answer:
First, we take scenario 1, in this scenario, the one end of the spring scale is attached to the post and the other end is pulled by a person, which means that there is no net force acting on it. Now in scenario 2, the post is replaced by the person with one end connected to another person. In scenario 1, if the person is pulling the spring scale to the right with force F, then there must be a tension force generated in the string F attaching the spring scale to the post in order for the spring scale to remain motionless.
Therefore, this shows that the same forces are acting on the spring scale in both scenarios. So if the spring scale reads $50\;{\rm{N}}$ in scenario 1, then it must also read $50\;{\rm{N}}$ in scenario 2. There are no effects of changing the length of the pieces of string. The length has no effect on the tension force in a string.

Note:
In this question, students make sure that there is no effect on the length of the string. The same force is applied on the spring scale in both scenarios. The spring scale shows the same force, whether it is attached to the post or any other person.